Module keras.api.keras.optimizers

Public API for tf.keras.optimizers namespace.

Expand source code
# This file is MACHINE GENERATED! Do not edit.
# Generated by: tensorflow/python/tools/api/generator/create_python_api.py script.
"""Public API for tf.keras.optimizers namespace.
"""

from __future__ import print_function as _print_function

import sys as _sys

from keras.api.keras.optimizers import schedules
from keras.optimizer_v2.adadelta import Adadelta
from keras.optimizer_v2.adagrad import Adagrad
from keras.optimizer_v2.adam import Adam
from keras.optimizer_v2.adamax import Adamax
from keras.optimizer_v2.ftrl import Ftrl
from keras.optimizer_v2.gradient_descent import SGD
from keras.optimizer_v2.nadam import Nadam
from keras.optimizer_v2.optimizer_v2 import OptimizerV2 as Optimizer
from keras.optimizer_v2.rmsprop import RMSprop
from keras.optimizers import deserialize
from keras.optimizers import get
from keras.optimizers import serialize

del _print_function

from tensorflow.python.util import module_wrapper as _module_wrapper

if not isinstance(_sys.modules[__name__], _module_wrapper.TFModuleWrapper):
  _sys.modules[__name__] = _module_wrapper.TFModuleWrapper(
      _sys.modules[__name__], "keras.optimizers", public_apis=None, deprecation=True,
      has_lite=False)

Sub-modules

keras.api.keras.optimizers.schedules

Public API for tf.keras.optimizers.schedules namespace.

Functions

def deserialize(config, custom_objects=None)

Inverse of the serialize() function.

Args

config
Optimizer configuration dictionary.
custom_objects
Optional dictionary mapping names (strings) to custom objects (classes and functions) to be considered during deserialization.

Returns

A Keras Optimizer instance.

Expand source code
@keras_export('keras.optimizers.deserialize')
def deserialize(config, custom_objects=None):
  """Inverse of the `serialize` function.

  Args:
      config: Optimizer configuration dictionary.
      custom_objects: Optional dictionary mapping names (strings) to custom
        objects (classes and functions) to be considered during deserialization.

  Returns:
      A Keras Optimizer instance.
  """
  # loss_scale_optimizer has a direct dependency of optimizer, import here
  # rather than top to avoid the cyclic dependency.
  from keras.mixed_precision import loss_scale_optimizer  # pylint: disable=g-import-not-at-top
  all_classes = {
      'adadelta': adadelta_v2.Adadelta,
      'adagrad': adagrad_v2.Adagrad,
      'adam': adam_v2.Adam,
      'adamax': adamax_v2.Adamax,
      'nadam': nadam_v2.Nadam,
      'rmsprop': rmsprop_v2.RMSprop,
      'sgd': gradient_descent_v2.SGD,
      'ftrl': ftrl.Ftrl,
      'lossscaleoptimizer': loss_scale_optimizer.LossScaleOptimizer,
      # LossScaleOptimizerV1 deserializes into LossScaleOptimizer, as
      # LossScaleOptimizerV1 will be removed soon but deserializing it will
      # still be supported.
      'lossscaleoptimizerv1': loss_scale_optimizer.LossScaleOptimizer,
  }

  # Make deserialization case-insensitive for built-in optimizers.
  if config['class_name'].lower() in all_classes:
    config['class_name'] = config['class_name'].lower()
  return deserialize_keras_object(
      config,
      module_objects=all_classes,
      custom_objects=custom_objects,
      printable_module_name='optimizer')
def get(identifier)

Retrieves a Keras Optimizer instance.

Args

identifier
Optimizer identifier, one of - String: name of an optimizer - Dictionary: configuration dictionary. - Keras Optimizer instance (it will be returned unchanged). - TensorFlow Optimizer instance (it will be wrapped as a Keras Optimizer).

Returns

A Keras Optimizer instance.

Raises

ValueError
If identifier cannot be interpreted.
Expand source code
@keras_export('keras.optimizers.get')
def get(identifier):
  """Retrieves a Keras Optimizer instance.

  Args:
      identifier: Optimizer identifier, one of
          - String: name of an optimizer
          - Dictionary: configuration dictionary. - Keras Optimizer instance (it
            will be returned unchanged). - TensorFlow Optimizer instance (it
            will be wrapped as a Keras Optimizer).

  Returns:
      A Keras Optimizer instance.

  Raises:
      ValueError: If `identifier` cannot be interpreted.
  """
  if isinstance(identifier, (Optimizer, optimizer_v2.OptimizerV2)):
    return identifier
  # Wrap legacy TF optimizer instances
  elif isinstance(identifier, tf.compat.v1.train.Optimizer):
    opt = TFOptimizer(identifier)
    backend.track_tf_optimizer(opt)
    return opt
  elif isinstance(identifier, dict):
    return deserialize(identifier)
  elif isinstance(identifier, str):
    config = {'class_name': str(identifier), 'config': {}}
    return deserialize(config)
  else:
    raise ValueError(
        'Could not interpret optimizer identifier: {}'.format(identifier))
def serialize(optimizer)

Serialize the optimizer configuration to JSON compatible python dict.

The configuration can be used for persistence and reconstruct the OptimizerV2 instance again.

>>> tf.keras.optimizers.serialize(tf.keras.optimizers.SGD())
{'class_name': 'SGD', 'config': {'name': 'SGD', 'learning_rate': 0.01,
                                 'decay': 0.0, 'momentum': 0.0,
                                 'nesterov': False}}

Args

optimizer
An OptimizerV2 instance to serialize.

Returns

Python dict which contains the configuration of the input optimizer.

Expand source code
@keras_export('keras.optimizers.serialize')
def serialize(optimizer):
  """Serialize the optimizer configuration to JSON compatible python dict.

  The configuration can be used for persistence and reconstruct the `Optimizer`
  instance again.

  >>> tf.keras.optimizers.serialize(tf.keras.optimizers.SGD())
  {'class_name': 'SGD', 'config': {'name': 'SGD', 'learning_rate': 0.01,
                                   'decay': 0.0, 'momentum': 0.0,
                                   'nesterov': False}}

  Args:
    optimizer: An `Optimizer` instance to serialize.

  Returns:
    Python dict which contains the configuration of the input optimizer.
  """
  return serialize_keras_object(optimizer)

Classes

class Adadelta (learning_rate=0.001, rho=0.95, epsilon=1e-07, name='Adadelta', **kwargs)

Optimizer that implements the Adadelta algorithm.

Adadelta optimization is a stochastic gradient descent method that is based on adaptive learning rate per dimension to address two drawbacks:

  • The continual decay of learning rates throughout training.
  • The need for a manually selected global learning rate.

Adadelta is a more robust extension of Adagrad that adapts learning rates based on a moving window of gradient updates, instead of accumulating all past gradients. This way, Adadelta continues learning even when many updates have been done. Compared to Adagrad, in the original version of Adadelta you don't have to set an initial learning rate. In this version, the initial learning rate can be set, as in most other Keras optimizers.

Args

learning_rate
Initial value for the learning rate: either a floating point value, or a tf.keras.optimizers.schedules.LearningRateSchedule instance. Defaults to 0.001. Note that Adadelta tends to benefit from higher initial learning rate values compared to other optimizers. To match the exact form in the original paper, use 1.0.
rho
A Tensor or a floating point value. The decay rate.
epsilon
Small floating point value used to maintain numerical stability.
name
Optional name prefix for the operations created when applying gradients. Defaults to "Adadelta".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm and represents the maximum norm of each parameter; "clipvalue" (float) clips gradient by value and represents the maximum absolute value of each parameter.

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Adadelta(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the Adadelta algorithm.

  Adadelta optimization is a stochastic gradient descent method that is based on
  adaptive learning rate per dimension to address two drawbacks:

  - The continual decay of learning rates throughout training.
  - The need for a manually selected global learning rate.

  Adadelta is a more robust extension of Adagrad that adapts learning rates
  based on a moving window of gradient updates, instead of accumulating all
  past gradients. This way, Adadelta continues learning even when many updates
  have been done. Compared to Adagrad, in the original version of Adadelta you
  don't have to set an initial learning rate. In this version, the initial
  learning rate can be set, as in most other Keras optimizers.

  Args:
    learning_rate: Initial value for the learning rate:
      either a floating point value,
      or a `tf.keras.optimizers.schedules.LearningRateSchedule` instance.
      Defaults to 0.001.
      Note that `Adadelta` tends to benefit from higher initial learning rate
      values compared to other optimizers.
      To match the exact form in the original paper, use 1.0.
    rho: A `Tensor` or a floating point value. The decay rate.
    epsilon: Small floating point value used to maintain numerical stability.
    name: Optional name prefix for the operations created when applying
      gradients.  Defaults to `"Adadelta"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm and represents
      the maximum norm of each parameter;
      `"clipvalue"` (float) clips gradient by value and represents the
      maximum absolute value of each parameter.

  Reference:
    - [Zeiler, 2012](http://arxiv.org/abs/1212.5701)
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               rho=0.95,
               epsilon=1e-7,
               name='Adadelta',
               **kwargs):
    super(Adadelta, self).__init__(name, **kwargs)
    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
    self._set_hyper('decay', self._initial_decay)
    self._set_hyper('rho', rho)
    self.epsilon = epsilon or backend_config.epsilon()

  def _create_slots(self, var_list):
    # Separate for-loops to respect the ordering of slot variables from v1.
    for v in var_list:
      self.add_slot(v, 'accum_grad')
    for v in var_list:
      self.add_slot(v, 'accum_var')

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(Adadelta, self)._prepare_local(var_device, var_dtype, apply_state)
    apply_state[(var_device, var_dtype)].update(
        dict(
            epsilon=tf.convert_to_tensor(
                self.epsilon, var_dtype),
            rho=tf.identity(self._get_hyper('rho', var_dtype))))

  def set_weights(self, weights):
    params = self.weights
    # Override set_weights for backward compatibility of Keras V1 optimizer
    # since it does not include iteration at head of the weight list. Set
    # iteration to 0.
    if len(params) == len(weights) + 1:
      weights = [np.array(0)] + weights
    super(Adadelta, self).set_weights(weights)

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    accum_grad = self.get_slot(var, 'accum_grad')
    accum_var = self.get_slot(var, 'accum_var')
    return tf.raw_ops.ResourceApplyAdadelta(
        var=var.handle,
        accum=accum_grad.handle,
        accum_update=accum_var.handle,
        lr=coefficients['lr_t'],
        rho=coefficients['rho'],
        epsilon=coefficients['epsilon'],
        grad=grad,
        use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    accum_grad = self.get_slot(var, 'accum_grad')
    accum_var = self.get_slot(var, 'accum_var')
    return tf.raw_ops.ResourceSparseApplyAdadelta(
        var=var.handle,
        accum=accum_grad.handle,
        accum_update=accum_var.handle,
        lr=coefficients['lr_t'],
        rho=coefficients['rho'],
        epsilon=coefficients['epsilon'],
        grad=grad,
        indices=indices,
        use_locking=self._use_locking)

  def get_config(self):
    config = super(Adadelta, self).get_config()
    config.update({
        'learning_rate': self._serialize_hyperparameter('learning_rate'),
        'decay': self._initial_decay,
        'rho': self._serialize_hyperparameter('rho'),
        'epsilon': self.epsilon,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Adagrad (learning_rate=0.001, initial_accumulator_value=0.1, epsilon=1e-07, name='Adagrad', **kwargs)

Optimizer that implements the Adagrad algorithm.

Adagrad is an optimizer with parameter-specific learning rates, which are adapted relative to how frequently a parameter gets updated during training. The more updates a parameter receives, the smaller the updates.

Args

learning_rate
Initial value for the learning rate: either a floating point value, or a tf.keras.optimizers.schedules.LearningRateSchedule instance. Defaults to 0.001. Note that Adagrad tends to benefit from higher initial learning rate values compared to other optimizers. To match the exact form in the original paper, use 1.0.
initial_accumulator_value
Floating point value. Starting value for the accumulators (per-parameter momentum values). Must be non-negative.
epsilon
Small floating point value used to maintain numerical stability.
name
Optional name prefix for the operations created when applying gradients. Defaults to "Adagrad".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm and represents the maximum L2 norm of each weight variable; "clipvalue" (float) clips gradient by value and represents the maximum absolute value of each weight variable.

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Adagrad(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the Adagrad algorithm.

  Adagrad is an optimizer with parameter-specific learning rates,
  which are adapted relative to how frequently a parameter gets
  updated during training. The more updates a parameter receives,
  the smaller the updates.

  Args:
    learning_rate: Initial value for the learning rate:
      either a floating point value,
      or a `tf.keras.optimizers.schedules.LearningRateSchedule` instance.
      Defaults to 0.001.
      Note that `Adagrad` tends to benefit from higher initial learning rate
      values compared to other optimizers.
      To match the exact form in the original paper, use 1.0.
    initial_accumulator_value: Floating point value.
      Starting value for the accumulators (per-parameter momentum values).
      Must be non-negative.
    epsilon: Small floating point value used to maintain numerical stability.
    name: Optional name prefix for the operations created when applying
      gradients.  Defaults to `"Adagrad"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm and represents
      the maximum L2 norm of each weight variable;
      `"clipvalue"` (float) clips gradient by value and represents the
      maximum absolute value of each weight variable.

  Reference:
    - [Duchi et al., 2011](
      http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf).
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               initial_accumulator_value=0.1,
               epsilon=1e-7,
               name='Adagrad',
               **kwargs):
    if initial_accumulator_value < 0.0:
      raise ValueError('initial_accumulator_value must be non-negative: %s' %
                       initial_accumulator_value)
    if epsilon is None:
      epsilon = backend_config.epsilon()
    super(Adagrad, self).__init__(name, **kwargs)
    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
    self._set_hyper('decay', self._initial_decay)
    self._initial_accumulator_value = initial_accumulator_value
    self.epsilon = epsilon or backend_config.epsilon()

  def _create_slots(self, var_list):
    for var in var_list:
      dtype = var.dtype.base_dtype
      init = tf.compat.v1.constant_initializer(
          self._initial_accumulator_value, dtype=dtype)
      self.add_slot(var, 'accumulator', init)

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(Adagrad, self)._prepare_local(var_device, var_dtype, apply_state)
    apply_state[(var_device, var_dtype)].update(
        dict(
            epsilon=tf.convert_to_tensor(
                self.epsilon, var_dtype),
            neg_lr_t=-apply_state[(var_device, var_dtype)]['lr_t'],
            zero=tf.zeros((), dtype=tf.int64)))

  def set_weights(self, weights):
    params = self.weights
    # Override set_weights for backward compatibility of Keras V1 optimizer
    # since it does not include iteration at head of the weight list. Set
    # iteration to 0.
    if len(params) == len(weights) + 1:
      weights = [np.array(0)] + weights
    super(Adagrad, self).set_weights(weights)

  @classmethod
  def from_config(cls, config, custom_objects=None):
    """Creates an optimizer from its config.

    This method is the reverse of `get_config`,
    capable of instantiating the same optimizer from the config
    dictionary.

    Args:
        config: A Python dictionary, typically the output of get_config.
        custom_objects: A Python dictionary mapping names to additional Python
          objects used to create this optimizer, such as a function used for a
          hyperparameter.

    Returns:
        An optimizer instance.
    """
    if 'initial_accumulator_value' not in config:
      config['initial_accumulator_value'] = 0.1
    if 'lr' in config:
      config['learning_rate'] = config.pop('lr')
    return cls(**config)

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    acc = self.get_slot(var, 'accumulator')
    return tf.raw_ops.ResourceApplyAdagradV2(
        var=var.handle,
        accum=acc.handle,
        lr=coefficients['lr_t'],
        epsilon=coefficients['epsilon'],
        grad=grad,
        use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    acc = self.get_slot(var, 'accumulator')
    return tf.raw_ops.ResourceSparseApplyAdagradV2(
        var=var.handle,
        accum=acc.handle,
        lr=coefficients['lr_t'],
        epsilon=coefficients['epsilon'],
        grad=grad,
        indices=indices,
        use_locking=self._use_locking)

  def get_config(self):
    config = super(Adagrad, self).get_config()
    config.update({
        'learning_rate': self._serialize_hyperparameter('learning_rate'),
        'decay': self._initial_decay,
        'initial_accumulator_value': self._initial_accumulator_value,
        'epsilon': self.epsilon,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Adam (learning_rate=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-07, amsgrad=False, name='Adam', **kwargs)

Optimizer that implements the Adam algorithm.

Adam optimization is a stochastic gradient descent method that is based on adaptive estimation of first-order and second-order moments.

According to Kingma et al., 2014, the method is "computationally efficient, has little memory requirement, invariant to diagonal rescaling of gradients, and is well suited for problems that are large in terms of data/parameters".

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use, The learning rate. Defaults to 0.001.
beta_1
A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use. The exponential decay rate for the 1st moment estimates. Defaults to 0.9.
beta_2
A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use, The exponential decay rate for the 2nd moment estimates. Defaults to 0.999.
epsilon
A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to 1e-7.
amsgrad
Boolean. Whether to apply AMSGrad variant of this algorithm from the paper "On the Convergence of Adam and beyond". Defaults to False.
name
Optional name for the operations created when applying gradients. Defaults to "Adam".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Usage:

>>> opt = tf.keras.optimizers.Adam(learning_rate=0.1)
>>> var1 = tf.Variable(10.0)
>>> loss = lambda: (var1 ** 2)/2.0       # d(loss)/d(var1) == var1
>>> step_count = opt.minimize(loss, [var1]).numpy()
>>> # The first step is `-learning_rate*sign(grad)`
>>> var1.numpy()
9.9

Reference

Notes:

The default value of 1e-7 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1. Note that since Adam uses the formulation just before Section 2.1 of the Kingma and Ba paper rather than the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon hat" in the paper.

The sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) does apply momentum to variable slices even if they were not used in the forward pass (meaning they have a gradient equal to zero). Momentum decay (beta1) is also applied to the entire momentum accumulator. This means that the sparse behavior is equivalent to the dense behavior (in contrast to some momentum implementations which ignore momentum unless a variable slice was actually used).

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Adam(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the Adam algorithm.

  Adam optimization is a stochastic gradient descent method that is based on
  adaptive estimation of first-order and second-order moments.

  According to
  [Kingma et al., 2014](http://arxiv.org/abs/1412.6980),
  the method is "*computationally
  efficient, has little memory requirement, invariant to diagonal rescaling of
  gradients, and is well suited for problems that are large in terms of
  data/parameters*".

  Args:
    learning_rate: A `Tensor`, floating point value, or a schedule that is a
      `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
      that takes no arguments and returns the actual value to use, The
      learning rate. Defaults to 0.001.
    beta_1: A float value or a constant float tensor, or a callable
      that takes no arguments and returns the actual value to use. The
      exponential decay rate for the 1st moment estimates. Defaults to 0.9.
    beta_2: A float value or a constant float tensor, or a callable
      that takes no arguments and returns the actual value to use, The
      exponential decay rate for the 2nd moment estimates. Defaults to 0.999.
    epsilon: A small constant for numerical stability. This epsilon is
      "epsilon hat" in the Kingma and Ba paper (in the formula just before
      Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
      1e-7.
    amsgrad: Boolean. Whether to apply AMSGrad variant of this algorithm from
      the paper "On the Convergence of Adam and beyond". Defaults to `False`.
    name: Optional name for the operations created when applying gradients.
      Defaults to `"Adam"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Usage:

  >>> opt = tf.keras.optimizers.Adam(learning_rate=0.1)
  >>> var1 = tf.Variable(10.0)
  >>> loss = lambda: (var1 ** 2)/2.0       # d(loss)/d(var1) == var1
  >>> step_count = opt.minimize(loss, [var1]).numpy()
  >>> # The first step is `-learning_rate*sign(grad)`
  >>> var1.numpy()
  9.9

  Reference:
    - [Kingma et al., 2014](http://arxiv.org/abs/1412.6980)
    - [Reddi et al., 2018](
        https://openreview.net/pdf?id=ryQu7f-RZ) for `amsgrad`.

  Notes:

  The default value of 1e-7 for epsilon might not be a good default in
  general. For example, when training an Inception network on ImageNet a
  current good choice is 1.0 or 0.1. Note that since Adam uses the
  formulation just before Section 2.1 of the Kingma and Ba paper rather than
  the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon
  hat" in the paper.

  The sparse implementation of this algorithm (used when the gradient is an
  IndexedSlices object, typically because of `tf.gather` or an embedding
  lookup in the forward pass) does apply momentum to variable slices even if
  they were not used in the forward pass (meaning they have a gradient equal
  to zero). Momentum decay (beta1) is also applied to the entire momentum
  accumulator. This means that the sparse behavior is equivalent to the dense
  behavior (in contrast to some momentum implementations which ignore momentum
  unless a variable slice was actually used).
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               beta_1=0.9,
               beta_2=0.999,
               epsilon=1e-7,
               amsgrad=False,
               name='Adam',
               **kwargs):
    super(Adam, self).__init__(name, **kwargs)
    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
    self._set_hyper('decay', self._initial_decay)
    self._set_hyper('beta_1', beta_1)
    self._set_hyper('beta_2', beta_2)
    self.epsilon = epsilon or backend_config.epsilon()
    self.amsgrad = amsgrad

  def _create_slots(self, var_list):
    # Create slots for the first and second moments.
    # Separate for-loops to respect the ordering of slot variables from v1.
    for var in var_list:
      self.add_slot(var, 'm')
    for var in var_list:
      self.add_slot(var, 'v')
    if self.amsgrad:
      for var in var_list:
        self.add_slot(var, 'vhat')

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(Adam, self)._prepare_local(var_device, var_dtype, apply_state)

    local_step = tf.cast(self.iterations + 1, var_dtype)
    beta_1_t = tf.identity(self._get_hyper('beta_1', var_dtype))
    beta_2_t = tf.identity(self._get_hyper('beta_2', var_dtype))
    beta_1_power = tf.pow(beta_1_t, local_step)
    beta_2_power = tf.pow(beta_2_t, local_step)
    lr = (apply_state[(var_device, var_dtype)]['lr_t'] *
          (tf.sqrt(1 - beta_2_power) / (1 - beta_1_power)))
    apply_state[(var_device, var_dtype)].update(
        dict(
            lr=lr,
            epsilon=tf.convert_to_tensor(
                self.epsilon, var_dtype),
            beta_1_t=beta_1_t,
            beta_1_power=beta_1_power,
            one_minus_beta_1_t=1 - beta_1_t,
            beta_2_t=beta_2_t,
            beta_2_power=beta_2_power,
            one_minus_beta_2_t=1 - beta_2_t))

  def set_weights(self, weights):
    params = self.weights
    # If the weights are generated by Keras V1 optimizer, it includes vhats
    # even without amsgrad, i.e, V1 optimizer has 3x + 1 variables, while V2
    # optimizer has 2x + 1 variables. Filter vhats out for compatibility.
    num_vars = int((len(params) - 1) / 2)
    if len(weights) == 3 * num_vars + 1:
      weights = weights[:len(params)]
    super(Adam, self).set_weights(weights)

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    m = self.get_slot(var, 'm')
    v = self.get_slot(var, 'v')

    if not self.amsgrad:
      return tf.raw_ops.ResourceApplyAdam(
          var=var.handle,
          m=m.handle,
          v=v.handle,
          beta1_power=coefficients['beta_1_power'],
          beta2_power=coefficients['beta_2_power'],
          lr=coefficients['lr_t'],
          beta1=coefficients['beta_1_t'],
          beta2=coefficients['beta_2_t'],
          epsilon=coefficients['epsilon'],
          grad=grad,
          use_locking=self._use_locking)
    else:
      vhat = self.get_slot(var, 'vhat')
      return tf.raw_ops.ResourceApplyAdamWithAmsgrad(
          var=var.handle,
          m=m.handle,
          v=v.handle,
          vhat=vhat.handle,
          beta1_power=coefficients['beta_1_power'],
          beta2_power=coefficients['beta_2_power'],
          lr=coefficients['lr_t'],
          beta1=coefficients['beta_1_t'],
          beta2=coefficients['beta_2_t'],
          epsilon=coefficients['epsilon'],
          grad=grad,
          use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    # m_t = beta1 * m + (1 - beta1) * g_t
    m = self.get_slot(var, 'm')
    m_scaled_g_values = grad * coefficients['one_minus_beta_1_t']
    m_t = tf.compat.v1.assign(m, m * coefficients['beta_1_t'],
                           use_locking=self._use_locking)
    with tf.control_dependencies([m_t]):
      m_t = self._resource_scatter_add(m, indices, m_scaled_g_values)

    # v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
    v = self.get_slot(var, 'v')
    v_scaled_g_values = (grad * grad) * coefficients['one_minus_beta_2_t']
    v_t = tf.compat.v1.assign(v, v * coefficients['beta_2_t'],
                           use_locking=self._use_locking)
    with tf.control_dependencies([v_t]):
      v_t = self._resource_scatter_add(v, indices, v_scaled_g_values)

    if not self.amsgrad:
      v_sqrt = tf.sqrt(v_t)
      var_update = tf.compat.v1.assign_sub(
          var, coefficients['lr'] * m_t / (v_sqrt + coefficients['epsilon']),
          use_locking=self._use_locking)
      return tf.group(*[var_update, m_t, v_t])
    else:
      v_hat = self.get_slot(var, 'vhat')
      v_hat_t = tf.maximum(v_hat, v_t)
      with tf.control_dependencies([v_hat_t]):
        v_hat_t = tf.compat.v1.assign(
            v_hat, v_hat_t, use_locking=self._use_locking)
      v_hat_sqrt = tf.sqrt(v_hat_t)
      var_update = tf.compat.v1.assign_sub(
          var,
          coefficients['lr'] * m_t / (v_hat_sqrt + coefficients['epsilon']),
          use_locking=self._use_locking)
      return tf.group(*[var_update, m_t, v_t, v_hat_t])

  def get_config(self):
    config = super(Adam, self).get_config()
    config.update({
        'learning_rate': self._serialize_hyperparameter('learning_rate'),
        'decay': self._initial_decay,
        'beta_1': self._serialize_hyperparameter('beta_1'),
        'beta_2': self._serialize_hyperparameter('beta_2'),
        'epsilon': self.epsilon,
        'amsgrad': self.amsgrad,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Adamax (learning_rate=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-07, name='Adamax', **kwargs)

Optimizer that implements the Adamax algorithm.

It is a variant of Adam based on the infinity norm. Default parameters follow those provided in the paper. Adamax is sometimes superior to adam, specially in models with embeddings.

Initialization:

m = 0  # Initialize initial 1st moment vector
v = 0  # Initialize the exponentially weighted infinity norm
t = 0  # Initialize timestep

The update rule for parameter w with gradient g is described at the end of section 7.1 of the paper:

t += 1
m = beta1 * m + (1 - beta) * g
v = max(beta2 * v, abs(g))
current_lr = learning_rate / (1 - beta1 ** t)
w = w - current_lr * m / (v + epsilon)

Similarly to Adam, the epsilon is added for numerical stability (especially to get rid of division by zero when v_t == 0).

In contrast to Adam, the sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) only updates variable slices and corresponding m_t, v_t terms when that part of the variable was used in the forward pass. This means that the sparse behavior is contrast to the dense behavior (similar to some momentum implementations which ignore momentum unless a variable slice was actually used).

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule. The learning rate.
beta_1
A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
beta_2
A float value or a constant float tensor. The exponential decay rate for the exponentially weighted infinity norm.
epsilon
A small constant for numerical stability.
name
Optional name for the operations created when applying gradients. Defaults to "Adamax".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Adamax(optimizer_v2.OptimizerV2):
  """Optimizer that implements the Adamax algorithm.

  It is a variant of Adam based on the infinity norm.
  Default parameters follow those provided in the paper.
  Adamax is sometimes superior to adam, specially in models with embeddings.

  Initialization:

  ```python
  m = 0  # Initialize initial 1st moment vector
  v = 0  # Initialize the exponentially weighted infinity norm
  t = 0  # Initialize timestep
  ```

  The update rule for parameter `w` with gradient `g` is
  described at the end of section 7.1 of the paper:

  ```python
  t += 1
  m = beta1 * m + (1 - beta) * g
  v = max(beta2 * v, abs(g))
  current_lr = learning_rate / (1 - beta1 ** t)
  w = w - current_lr * m / (v + epsilon)
  ```

  Similarly to `Adam`, the epsilon is added for numerical stability
  (especially to get rid of division by zero when `v_t == 0`).

  In contrast to `Adam`, the sparse implementation of this algorithm
  (used when the gradient is an IndexedSlices object, typically because of
  `tf.gather` or an embedding lookup in the forward pass) only updates
  variable slices and corresponding `m_t`, `v_t` terms when that part of
  the variable was used in the forward pass. This means that the sparse
  behavior is contrast to the dense behavior (similar to some momentum
  implementations which ignore momentum unless a variable slice was actually
  used).

  Args:
    learning_rate: A `Tensor`, floating point value, or a schedule that is a
      `tf.keras.optimizers.schedules.LearningRateSchedule`. The learning rate.
    beta_1: A float value or a constant float tensor. The exponential decay
      rate for the 1st moment estimates.
    beta_2: A float value or a constant float tensor. The exponential decay
      rate for the exponentially weighted infinity norm.
    epsilon: A small constant for numerical stability.
    name: Optional name for the operations created when applying gradients.
      Defaults to `"Adamax"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Reference:
    - [Kingma et al., 2014](http://arxiv.org/abs/1412.6980)
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               beta_1=0.9,
               beta_2=0.999,
               epsilon=1e-7,
               name='Adamax',
               **kwargs):
    super(Adamax, self).__init__(name, **kwargs)
    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
    self._set_hyper('decay', self._initial_decay)
    self._set_hyper('beta_1', beta_1)
    self._set_hyper('beta_2', beta_2)
    self.epsilon = epsilon or backend_config.epsilon()

  def _create_slots(self, var_list):
    # Separate for-loops to respect the ordering of slot variables from v1.
    for var in var_list:
      self.add_slot(var, 'm')  # Create slots for the first moments.
    for var in var_list:
      self.add_slot(var, 'v')  # Create slots for the second moments.

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(Adamax, self)._prepare_local(var_device, var_dtype, apply_state)

    local_step = tf.cast(self.iterations + 1, var_dtype)
    beta_1_t = tf.identity(self._get_hyper('beta_1', var_dtype))
    beta_2_t = tf.identity(self._get_hyper('beta_2', var_dtype))
    beta_1_power = tf.pow(beta_1_t, local_step)
    lr_t = apply_state[(var_device, var_dtype)]['lr_t']

    apply_state[(var_device, var_dtype)].update(
        dict(
            neg_scaled_lr=-lr_t / (1 - beta_1_power),
            epsilon=tf.convert_to_tensor(
                self.epsilon, var_dtype),
            beta_1_t=beta_1_t,
            beta_1_power=beta_1_power,
            one_minus_beta_1_t=1 - beta_1_t,
            beta_2_t=beta_2_t,
            zero=tf.zeros((), dtype=tf.int64)))

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    m = self.get_slot(var, 'm')
    v = self.get_slot(var, 'v')
    return tf.raw_ops.ResourceApplyAdaMax(
        var=var.handle,
        m=m.handle,
        v=v.handle,
        beta1_power=coefficients['beta_1_power'],
        lr=coefficients['lr_t'],
        beta1=coefficients['beta_1_t'],
        beta2=coefficients['beta_2_t'],
        epsilon=coefficients['epsilon'],
        grad=grad,
        use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    # m_t = beta1 * m + (1 - beta1) * g_t
    m = self.get_slot(var, 'm')
    m_slice = tf.gather(m, indices, axis=coefficients['zero'])
    m_t_slice = (m_slice * coefficients['beta_1_t'] +
                 grad * coefficients['one_minus_beta_1_t'])
    with tf.control_dependencies([m_t_slice]):
      m_t = self._resource_scatter_update(m, indices, m_t_slice)

    # u_t = max(beta2 * u, abs(g_t))
    v = self.get_slot(var, 'v')
    v_slice = tf.gather(v, indices, axis=coefficients['zero'])
    v_t_slice = tf.maximum(v_slice * coefficients['beta_2_t'],
                                 tf.abs(grad))
    with tf.control_dependencies([v_t_slice]):
      v_t = self._resource_scatter_update(v, indices, v_t_slice)
    # theta_t = theta - lr / (1 - beta1^t) * m_t / u_t
    var_slice = coefficients['neg_scaled_lr'] * (
        m_t_slice / (v_t_slice + coefficients['epsilon']))
    with tf.control_dependencies([var_slice]):
      var_update = self._resource_scatter_add(var, indices, var_slice)
    return tf.group(*[var_update, m_t, v_t])

  def get_config(self):
    config = super(Adamax, self).get_config()
    config.update({
        'learning_rate': self._serialize_hyperparameter('learning_rate'),
        'decay': self._initial_decay,
        'beta_1': self._serialize_hyperparameter('beta_1'),
        'beta_2': self._serialize_hyperparameter('beta_2'),
        'epsilon': self.epsilon,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Ftrl (learning_rate=0.001, learning_rate_power=-0.5, initial_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, name='Ftrl', l2_shrinkage_regularization_strength=0.0, beta=0.0, **kwargs)

Optimizer that implements the FTRL algorithm.

"Follow The Regularized Leader" (FTRL) is an optimization algorithm developed at Google for click-through rate prediction in the early 2010s. It is most suitable for shallow models with large and sparse feature spaces. The algorithm is described by McMahan et al., 2013. The Keras version has support for both online L2 regularization (the L2 regularization described in the paper above) and shrinkage-type L2 regularization (which is the addition of an L2 penalty to the loss function).

Initialization:

n = 0
sigma = 0
z = 0

Update rule for one variable w:

prev_n = n
n = n + g ** 2
sigma = (sqrt(n) - sqrt(prev_n)) / lr
z = z + g - sigma * w
if abs(z) < lambda_1:
  w = 0
else:
  w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2)

Notation:

  • lr is the learning rate
  • g is the gradient for the variable
  • lambda_1 is the L1 regularization strength
  • lambda_2 is the L2 regularization strength

Check the documentation for the l2_shrinkage_regularization_strength parameter for more details when shrinkage is enabled, in which case gradient is replaced with a gradient with shrinkage.

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule. The learning rate.
learning_rate_power
A float value, must be less or equal to zero. Controls how the learning rate decreases during training. Use zero for a fixed learning rate.
initial_accumulator_value
The starting value for accumulators. Only zero or positive values are allowed.
l1_regularization_strength
A float value, must be greater than or equal to zero. Defaults to 0.0.
l2_regularization_strength
A float value, must be greater than or equal to zero. Defaults to 0.0.
name
Optional name prefix for the operations created when applying gradients. Defaults to "Ftrl".
l2_shrinkage_regularization_strength
A float value, must be greater than or equal to zero. This differs from L2 above in that the L2 above is a stabilization penalty, whereas this L2 shrinkage is a magnitude penalty. When input is sparse shrinkage will only happen on the active weights.
beta
A float value, representing the beta value from the paper. Defaults to 0.0.
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Ftrl(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the FTRL algorithm.

  "Follow The Regularized Leader" (FTRL) is an optimization algorithm developed
  at Google for click-through rate prediction in the early 2010s. It is most
  suitable for shallow models with large and sparse feature spaces.
  The algorithm is described by
  [McMahan et al., 2013](https://research.google.com/pubs/archive/41159.pdf).
  The Keras version has support for both online L2 regularization
  (the L2 regularization described in the paper
  above) and shrinkage-type L2 regularization
  (which is the addition of an L2 penalty to the loss function).

  Initialization:

  ```python
  n = 0
  sigma = 0
  z = 0
  ```

  Update rule for one variable `w`:

  ```python
  prev_n = n
  n = n + g ** 2
  sigma = (sqrt(n) - sqrt(prev_n)) / lr
  z = z + g - sigma * w
  if abs(z) < lambda_1:
    w = 0
  else:
    w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2)
  ```

  Notation:

  - `lr` is the learning rate
  - `g` is the gradient for the variable
  - `lambda_1` is the L1 regularization strength
  - `lambda_2` is the L2 regularization strength

  Check the documentation for the `l2_shrinkage_regularization_strength`
  parameter for more details when shrinkage is enabled, in which case gradient
  is replaced with a gradient with shrinkage.

  Args:
    learning_rate: A `Tensor`, floating point value, or a schedule that is a
      `tf.keras.optimizers.schedules.LearningRateSchedule`. The learning rate.
    learning_rate_power: A float value, must be less or equal to zero.
      Controls how the learning rate decreases during training. Use zero for
      a fixed learning rate.
    initial_accumulator_value: The starting value for accumulators.
      Only zero or positive values are allowed.
    l1_regularization_strength: A float value, must be greater than or
      equal to zero. Defaults to 0.0.
    l2_regularization_strength: A float value, must be greater than or
      equal to zero. Defaults to 0.0.
    name: Optional name prefix for the operations created when applying
      gradients.  Defaults to `"Ftrl"`.
    l2_shrinkage_regularization_strength: A float value, must be greater than
      or equal to zero. This differs from L2 above in that the L2 above is a
      stabilization penalty, whereas this L2 shrinkage is a magnitude penalty.
      When input is sparse shrinkage will only happen on the active weights.
    beta: A float value, representing the beta value from the paper.
      Defaults to 0.0.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Reference:
    - [McMahan et al., 2013](
      https://research.google.com/pubs/archive/41159.pdf)
  """

  def __init__(self,
               learning_rate=0.001,
               learning_rate_power=-0.5,
               initial_accumulator_value=0.1,
               l1_regularization_strength=0.0,
               l2_regularization_strength=0.0,
               name='Ftrl',
               l2_shrinkage_regularization_strength=0.0,
               beta=0.0,
               **kwargs):
    super(Ftrl, self).__init__(name, **kwargs)

    if initial_accumulator_value < 0.0:
      raise ValueError(
          'initial_accumulator_value %f needs to be positive or zero' %
          initial_accumulator_value)
    if learning_rate_power > 0.0:
      raise ValueError('learning_rate_power %f needs to be negative or zero' %
                       learning_rate_power)
    if l1_regularization_strength < 0.0:
      raise ValueError(
          'l1_regularization_strength %f needs to be positive or zero' %
          l1_regularization_strength)
    if l2_regularization_strength < 0.0:
      raise ValueError(
          'l2_regularization_strength %f needs to be positive or zero' %
          l2_regularization_strength)
    if l2_shrinkage_regularization_strength < 0.0:
      raise ValueError(
          'l2_shrinkage_regularization_strength %f needs to be positive'
          ' or zero' % l2_shrinkage_regularization_strength)

    self._set_hyper('learning_rate', learning_rate)
    self._set_hyper('decay', self._initial_decay)
    self._set_hyper('learning_rate_power', learning_rate_power)
    self._set_hyper('l1_regularization_strength', l1_regularization_strength)
    self._set_hyper('l2_regularization_strength', l2_regularization_strength)
    self._set_hyper('beta', beta)
    self._initial_accumulator_value = initial_accumulator_value
    self._l2_shrinkage_regularization_strength = (
        l2_shrinkage_regularization_strength)

  def _create_slots(self, var_list):
    # Create the "accum" and "linear" slots.
    for var in var_list:
      dtype = var.dtype.base_dtype
      init = tf.compat.v1.constant_initializer(
          self._initial_accumulator_value, dtype=dtype)
      self.add_slot(var, 'accumulator', init)
      self.add_slot(var, 'linear')

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(Ftrl, self)._prepare_local(var_device, var_dtype, apply_state)
    apply_state[(var_device, var_dtype)].update(
        dict(
            learning_rate_power=tf.identity(
                self._get_hyper('learning_rate_power', var_dtype)),
            l1_regularization_strength=tf.identity(
                self._get_hyper('l1_regularization_strength', var_dtype)),
            l2_regularization_strength=tf.identity(
                self._get_hyper('l2_regularization_strength', var_dtype)),
            beta=tf.identity(self._get_hyper('beta', var_dtype)),
            l2_shrinkage_regularization_strength=tf.cast(
                self._l2_shrinkage_regularization_strength, var_dtype)))

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    # Adjust L2 regularization strength to include beta to avoid the underlying
    # TensorFlow ops needing to include it.
    adjusted_l2_regularization_strength = (
        coefficients['l2_regularization_strength'] + coefficients['beta'] /
        (2. * coefficients['lr_t']))

    accum = self.get_slot(var, 'accumulator')
    linear = self.get_slot(var, 'linear')

    if self._l2_shrinkage_regularization_strength <= 0.0:
      return tf.raw_ops.ResourceApplyFtrl(
          var=var.handle,
          accum=accum.handle,
          linear=linear.handle,
          grad=grad,
          lr=coefficients['lr_t'],
          l1=coefficients['l1_regularization_strength'],
          l2=adjusted_l2_regularization_strength,
          lr_power=coefficients['learning_rate_power'],
          use_locking=self._use_locking)
    else:
      return tf.raw_ops.ResourceApplyFtrlV2(
          var=var.handle,
          accum=accum.handle,
          linear=linear.handle,
          grad=grad,
          lr=coefficients['lr_t'],
          l1=coefficients['l1_regularization_strength'],
          l2=adjusted_l2_regularization_strength,
          l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'],
          lr_power=coefficients['learning_rate_power'],
          use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    # Adjust L2 regularization strength to include beta to avoid the underlying
    # TensorFlow ops needing to include it.
    adjusted_l2_regularization_strength = (
        coefficients['l2_regularization_strength'] + coefficients['beta'] /
        (2. * coefficients['lr_t']))

    accum = self.get_slot(var, 'accumulator')
    linear = self.get_slot(var, 'linear')

    if self._l2_shrinkage_regularization_strength <= 0.0:
      return tf.raw_ops.ResourceSparseApplyFtrl(
          var=var.handle,
          accum=accum.handle,
          linear=linear.handle,
          grad=grad,
          indices=indices,
          lr=coefficients['lr_t'],
          l1=coefficients['l1_regularization_strength'],
          l2=adjusted_l2_regularization_strength,
          lr_power=coefficients['learning_rate_power'],
          use_locking=self._use_locking)
    else:
      return tf.raw_ops.ResourceSparseApplyFtrlV2(
          var=var.handle,
          accum=accum.handle,
          linear=linear.handle,
          grad=grad,
          indices=indices,
          lr=coefficients['lr_t'],
          l1=coefficients['l1_regularization_strength'],
          l2=adjusted_l2_regularization_strength,
          l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'],
          lr_power=coefficients['learning_rate_power'],
          use_locking=self._use_locking)

  def get_config(self):
    config = super(Ftrl, self).get_config()
    config.update({
        'learning_rate':
            self._serialize_hyperparameter('learning_rate'),
        'decay':
            self._initial_decay,
        'initial_accumulator_value':
            self._initial_accumulator_value,
        'learning_rate_power':
            self._serialize_hyperparameter('learning_rate_power'),
        'l1_regularization_strength':
            self._serialize_hyperparameter('l1_regularization_strength'),
        'l2_regularization_strength':
            self._serialize_hyperparameter('l2_regularization_strength'),
        'beta':
            self._serialize_hyperparameter('beta'),
        'l2_shrinkage_regularization_strength':
            self._l2_shrinkage_regularization_strength,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Nadam (learning_rate=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-07, name='Nadam', **kwargs)

Optimizer that implements the NAdam algorithm. Much like Adam is essentially RMSprop with momentum, Nadam is Adam with Nesterov momentum.

Args

learning_rate
A Tensor or a floating point value. The learning rate.
beta_1
A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
beta_2
A float value or a constant float tensor. The exponential decay rate for the exponentially weighted infinity norm.
epsilon
A small constant for numerical stability.
name
Optional name for the operations created when applying gradients. Defaults to "Nadam".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Usage Example:

opt = tf.keras.optimizers.Nadam(learning_rate=0.2) var1 = tf.Variable(10.0) loss = lambda: (var1 ** 2) / 2.0 step_count = opt.minimize(loss, [var1]).numpy() "{:.1f}".format(var1.numpy()) 9.8

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class Nadam(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the NAdam algorithm.
  Much like Adam is essentially RMSprop with momentum, Nadam is Adam with
  Nesterov momentum.

  Args:
    learning_rate: A Tensor or a floating point value.  The learning rate.
    beta_1: A float value or a constant float tensor. The exponential decay
      rate for the 1st moment estimates.
    beta_2: A float value or a constant float tensor. The exponential decay
      rate for the exponentially weighted infinity norm.
    epsilon: A small constant for numerical stability.
    name: Optional name for the operations created when applying gradients.
      Defaults to `"Nadam"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Usage Example:
    >>> opt = tf.keras.optimizers.Nadam(learning_rate=0.2)
    >>> var1 = tf.Variable(10.0)
    >>> loss = lambda: (var1 ** 2) / 2.0
    >>> step_count = opt.minimize(loss, [var1]).numpy()
    >>> "{:.1f}".format(var1.numpy())
    9.8

  Reference:
    - [Dozat, 2015](http://cs229.stanford.edu/proj2015/054_report.pdf).
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               beta_1=0.9,
               beta_2=0.999,
               epsilon=1e-7,
               name='Nadam',
               **kwargs):
    # Backwards compatibility with keras NAdam optimizer.
    kwargs['decay'] = kwargs.pop('schedule_decay', 0.004)
    learning_rate = kwargs.get('lr', learning_rate)
    if isinstance(learning_rate, learning_rate_schedule.LearningRateSchedule):
      raise ValueError('The Nadam optimizer does not support '
                       'tf.keras.optimizers.LearningRateSchedules as the '
                       'learning rate.')

    super(Nadam, self).__init__(name, **kwargs)
    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
    self._set_hyper('decay', self._initial_decay)
    self._set_hyper('beta_1', beta_1)
    self._set_hyper('beta_2', beta_2)
    self.epsilon = epsilon or backend_config.epsilon()
    self._m_cache = None

  def _create_slots(self, var_list):
    var_dtype = var_list[0].dtype.base_dtype
    if self._m_cache is None:
      self._m_cache = self.add_weight(
          'momentum_cache',
          shape=[],
          dtype=var_dtype,
          initializer='ones',
          trainable=False,
          aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA)
      self._weights.append(self._m_cache)
    # Separate for-loops to respect the ordering of slot variables from v1.
    for var in var_list:
      # Create slots for the first moments.
      self.add_slot(var, 'm')
    for var in var_list:
      # Create slots for the second moments.
      self.add_slot(var, 'v')

  def _prepare_local(self, var_device, var_dtype, apply_state):
    lr_t = tf.identity(self._get_hyper('learning_rate', var_dtype))
    beta_1_t = tf.identity(self._get_hyper('beta_1', var_dtype))
    beta_2_t = tf.identity(self._get_hyper('beta_2', var_dtype))
    local_step = tf.cast(self.iterations + 1, var_dtype)
    next_step = tf.cast(self.iterations + 2, var_dtype)

    decay_base = tf.cast(0.96, var_dtype)

    m_t = beta_1_t * (1. - 0.5 * (
        tf.pow(decay_base, self._initial_decay * local_step)))
    m_t_1 = beta_1_t * (1. - 0.5 * (
        tf.pow(decay_base, self._initial_decay * next_step)))

    m_schedule_new = tf.cast(self._m_cache_read, var_dtype) * m_t
    if var_dtype is self._m_cache.dtype:
      m_schedule_new = tf.identity(tf.compat.v1.assign(
          self._m_cache, m_schedule_new, use_locking=self._use_locking))
    m_schedule_next = m_schedule_new * m_t_1

    apply_state[(var_device, var_dtype)] = dict(
        lr_t=lr_t,
        neg_lr_t=-lr_t,  # pylint: disable=invalid-unary-operand-type
        epsilon=tf.convert_to_tensor(self.epsilon, var_dtype),
        beta_1_t=beta_1_t,
        beta_2_t=beta_2_t,
        m_t=m_t,
        m_t_1=m_t_1,
        one_minus_beta_1_t=1 - beta_1_t,
        one_minus_beta_2_t=1 - beta_2_t,
        one_minus_m_t=1. - m_t,
        one_minus_m_schedule_new=1. - m_schedule_new,
        one_minus_m_schedule_next=1. - m_schedule_next,
        v_t_prime_denominator=1. - tf.pow(beta_2_t, local_step),
    )

  def _prepare(self, var_list):
    # Get the value of the momentum cache before starting to apply gradients.
    self._m_cache_read = tf.identity(self._m_cache)
    return super(Nadam, self)._prepare(var_list)

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    m = self.get_slot(var, 'm')
    v = self.get_slot(var, 'v')

    g_prime = grad / coefficients['one_minus_m_schedule_new']
    m_t = (coefficients['beta_1_t'] * m +
           coefficients['one_minus_beta_1_t'] * grad)
    m_t = tf.compat.v1.assign(m, m_t, use_locking=self._use_locking)
    m_t_prime = m_t / coefficients['one_minus_m_schedule_next']
    v_t = (coefficients['beta_2_t'] * v +
           coefficients['one_minus_beta_2_t'] * tf.square(grad))
    v_t = tf.compat.v1.assign(v, v_t, use_locking=self._use_locking)
    v_t_prime = v_t / coefficients['v_t_prime_denominator']
    m_t_bar = (coefficients['one_minus_m_t'] * g_prime +
               coefficients['m_t_1'] * m_t_prime)
    var_t = var - coefficients['lr_t'] * m_t_bar / (
        tf.sqrt(v_t_prime) + coefficients['epsilon'])
    return tf.compat.v1.assign(var, var_t, use_locking=self._use_locking).op

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    m = self.get_slot(var, 'm')
    v = self.get_slot(var, 'v')

    g_prime = grad / coefficients['one_minus_m_schedule_new']

    # m_t = beta1 * m + (1 - beta1) * g_t
    m_scaled_g_values = grad * coefficients['one_minus_beta_1_t']
    m_t = tf.compat.v1.assign(m, m * coefficients['beta_1_t'],
                           use_locking=self._use_locking)

    with tf.control_dependencies([m_t]):
      m_t = self._resource_scatter_add(m, indices, m_scaled_g_values)
      m_t_slice = tf.gather(m_t, indices)

    m_t_prime = m_t_slice / coefficients['one_minus_m_schedule_next']
    m_t_bar = (coefficients['one_minus_m_t'] * g_prime +
               coefficients['m_t_1'] * m_t_prime)

    # v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
    v_scaled_g_values = (grad * grad) * coefficients['one_minus_beta_2_t']
    v_t = tf.compat.v1.assign(v, v * coefficients['beta_2_t'],
                           use_locking=self._use_locking)

    with tf.control_dependencies([v_t]):
      v_t = self._resource_scatter_add(v, indices, v_scaled_g_values)
      v_t_slice = tf.gather(v_t, indices)

    v_t_prime = v_t_slice / coefficients['v_t_prime_denominator']
    v_prime_sqrt_plus_eps = tf.sqrt(v_t_prime) + coefficients['epsilon']

    var_update = self._resource_scatter_add(
        var, indices,
        coefficients['neg_lr_t'] * m_t_bar / v_prime_sqrt_plus_eps)
    return tf.group(*[var_update, m_t_bar, v_t])

  def get_config(self):
    config = super(Nadam, self).get_config()
    config.update({
        'learning_rate': self._serialize_hyperparameter('learning_rate'),
        'decay': self._initial_decay,
        'beta_1': self._serialize_hyperparameter('beta_1'),
        'beta_2': self._serialize_hyperparameter('beta_2'),
        'epsilon': self.epsilon,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class Optimizer (name, gradient_aggregator=None, gradient_transformers=None, **kwargs)

Base class for Keras optimizers.

You should not use this class directly, but instead instantiate one of its subclasses such as tf.keras.optimizers.SGD, tf.keras.optimizers.Adam, etc.

Usage

# Create an optimizer with the desired parameters.
opt = tf.keras.optimizers.SGD(learning_rate=0.1)
# `loss` is a callable that takes no argument and returns the value
# to minimize.
loss = lambda: 3 * var1 * var1 + 2 * var2 * var2
# In graph mode, returns op that minimizes the loss by updating the listed
# variables.
opt_op = opt.minimize(loss, var_list=[var1, var2])
opt_op.run()
# In eager mode, simply call minimize to update the list of variables.
opt.minimize(loss, var_list=[var1, var2])

Usage in custom training loops

In Keras models, sometimes variables are created when the model is first called, instead of construction time. Examples include 1) sequential models without input shape pre-defined, or 2) subclassed models. Pass var_list as callable in these cases.

Example:

opt = tf.keras.optimizers.SGD(learning_rate=0.1)
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(num_hidden, activation='relu'))
model.add(tf.keras.layers.Dense(num_classes, activation='sigmoid'))
loss_fn = lambda: tf.keras.losses.mse(model(input), output)
var_list_fn = lambda: model.trainable_weights
for input, output in data:
  opt.minimize(loss_fn, var_list_fn)

Processing gradients before applying them

Calling minimize() takes care of both computing the gradients and applying them to the variables. If you want to process the gradients before applying them you can instead use the optimizer in three steps:

  1. Compute the gradients with tf.GradientTape.
  2. Process the gradients as you wish.
  3. Apply the processed gradients with apply_gradients().

Example:

# Create an optimizer.
opt = tf.keras.optimizers.SGD(learning_rate=0.1)

# Compute the gradients for a list of variables.
with tf.GradientTape() as tape:
  loss = <call_loss_function>
vars = <list_of_variables>
grads = tape.gradient(loss, vars)

# Process the gradients, for example cap them, etc.
# capped_grads = [MyCapper(g) for g in grads]
processed_grads = [process_gradient(g) for g in grads]

# Ask the optimizer to apply the processed gradients.
opt.apply_gradients(zip(processed_grads, var_list))

Use with tf.distribute.Strategy

This optimizer class is tf.distribute.Strategy aware, which means it automatically sums gradients across all replicas. To average gradients, you divide your loss by the global batch size, which is done automatically if you use tf.keras built-in training or evaluation loops. See the reduction argument of your loss which should be set to tf.keras.losses.Reduction.SUM_OVER_BATCH_SIZE for averaging or tf.keras.losses.Reduction.SUM for not.

To aggregate gradients yourself, call apply_gradients with experimental_aggregate_gradients set to False. This is useful if you need to process aggregated gradients.

If you are not using these and you want to average gradients, you should use tf.math.reduce_sum to add up your per-example losses and then divide by the global batch size. Note that when using tf.distribute.Strategy, the first component of a tensor's shape is the replica-local batch size, which is off by a factor equal to the number of replicas being used to compute a single step. As a result, using tf.math.reduce_mean will give the wrong answer, resulting in gradients that can be many times too big.

Variable Constraints

All Keras optimizers respect variable constraints. If constraint function is passed to any variable, the constraint will be applied to the variable after the gradient has been applied to the variable. Important: If gradient is sparse tensor, variable constraint is not supported.

Thread Compatibility

The entire optimizer is currently thread compatible, not thread-safe. The user needs to perform synchronization if necessary.

Slots

Many optimizer subclasses, such as Adam and Adagrad allocate and manage additional variables associated with the variables to train. These are called Slots. Slots have names and you can ask the optimizer for the names of the slots that it uses. Once you have a slot name you can ask the optimizer for the variable it created to hold the slot value.

This can be useful if you want to log debug a training algorithm, report stats about the slots, etc.

Hyperparameters

These are arguments passed to the optimizer subclass constructor (the __init__ method), and then passed to self._set_hyper(). They can be either regular Python values (like 1.0), tensors, or callables. If they are callable, the callable will be called during apply_gradients() to get the value for the hyper parameter.

Hyperparameters can be overwritten through user code:

Example:

# Create an optimizer with the desired parameters.
opt = tf.keras.optimizers.SGD(learning_rate=0.1)
# `loss` is a callable that takes no argument and returns the value
# to minimize.
loss = lambda: 3 * var1 + 2 * var2
# In eager mode, simply call minimize to update the list of variables.
opt.minimize(loss, var_list=[var1, var2])
# update learning rate
opt.learning_rate = 0.05
opt.minimize(loss, var_list=[var1, var2])

Callable learning rate

Optimizer accepts a callable learning rate in two ways. The first way is through built-in or customized tf.keras.optimizers.schedules.LearningRateSchedule. The schedule will be called on each iteration with schedule(iteration), a tf.Variable owned by the optimizer.

Example:

>>> var = tf.Variable(np.random.random(size=(1,)))
>>> learning_rate = tf.keras.optimizers.schedules.ExponentialDecay(
... initial_learning_rate=.01, decay_steps=20, decay_rate=.1)
>>> opt = tf.keras.optimizers.SGD(learning_rate=learning_rate)
>>> loss = lambda: 3 * var
>>> opt.minimize(loss, var_list=[var])
<tf.Variable...

The second way is through a callable function that does not accept any arguments.

Example:

>>> var = tf.Variable(np.random.random(size=(1,)))
>>> def lr_callable():
...   return .1
>>> opt = tf.keras.optimizers.SGD(learning_rate=lr_callable)
>>> loss = lambda: 3 * var
>>> opt.minimize(loss, var_list=[var])
<tf.Variable...

Creating a custom optimizer

If you intend to create your own optimization algorithm, simply inherit from this class and override the following methods:

  • _resource_apply_dense (update variable given gradient tensor is a dense tf.Tensor)
  • _resource_apply_sparse (update variable given gradient tensor is a sparse tf.IndexedSlices. The most common way for this to happen is if you are taking the gradient through a tf.gather.)
  • _create_slots (if your optimizer algorithm requires additional variables)
  • get_config (serialization of the optimizer, include all hyper parameters)

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class OptimizerV2(tf.__internal__.tracking.Trackable):
  """Base class for Keras optimizers.

  You should not use this class directly, but instead instantiate one of its
  subclasses such as `tf.keras.optimizers.SGD`, `tf.keras.optimizers.Adam`, etc.

  ### Usage

  ```python
  # Create an optimizer with the desired parameters.
  opt = tf.keras.optimizers.SGD(learning_rate=0.1)
  # `loss` is a callable that takes no argument and returns the value
  # to minimize.
  loss = lambda: 3 * var1 * var1 + 2 * var2 * var2
  # In graph mode, returns op that minimizes the loss by updating the listed
  # variables.
  opt_op = opt.minimize(loss, var_list=[var1, var2])
  opt_op.run()
  # In eager mode, simply call minimize to update the list of variables.
  opt.minimize(loss, var_list=[var1, var2])
  ```

  ### Usage in custom training loops

  In Keras models, sometimes variables are created when the model is first
  called, instead of construction time. Examples include 1) sequential models
  without input shape pre-defined, or 2) subclassed models. Pass var_list as
  callable in these cases.

  Example:

  ```python
  opt = tf.keras.optimizers.SGD(learning_rate=0.1)
  model = tf.keras.Sequential()
  model.add(tf.keras.layers.Dense(num_hidden, activation='relu'))
  model.add(tf.keras.layers.Dense(num_classes, activation='sigmoid'))
  loss_fn = lambda: tf.keras.losses.mse(model(input), output)
  var_list_fn = lambda: model.trainable_weights
  for input, output in data:
    opt.minimize(loss_fn, var_list_fn)
  ```

  ### Processing gradients before applying them

  Calling `minimize()` takes care of both computing the gradients and
  applying them to the variables.  If you want to process the gradients
  before applying them you can instead use the optimizer in three steps:

  1.  Compute the gradients with `tf.GradientTape`.
  2.  Process the gradients as you wish.
  3.  Apply the processed gradients with `apply_gradients()`.

  Example:

  ```python
  # Create an optimizer.
  opt = tf.keras.optimizers.SGD(learning_rate=0.1)

  # Compute the gradients for a list of variables.
  with tf.GradientTape() as tape:
    loss = <call_loss_function>
  vars = <list_of_variables>
  grads = tape.gradient(loss, vars)

  # Process the gradients, for example cap them, etc.
  # capped_grads = [MyCapper(g) for g in grads]
  processed_grads = [process_gradient(g) for g in grads]

  # Ask the optimizer to apply the processed gradients.
  opt.apply_gradients(zip(processed_grads, var_list))
  ```

  ### Use with `tf.distribute.Strategy`

  This optimizer class is `tf.distribute.Strategy` aware, which means it
  automatically sums gradients across all replicas. To average gradients,
  you divide your loss by the global batch size, which is done
  automatically if you use `tf.keras` built-in training or evaluation loops.
  See the `reduction` argument of your loss which should be set to
  `tf.keras.losses.Reduction.SUM_OVER_BATCH_SIZE` for averaging or
  `tf.keras.losses.Reduction.SUM` for not.

  To aggregate gradients yourself, call `apply_gradients` with
  `experimental_aggregate_gradients` set to False. This is useful if you need to
  process aggregated gradients.

  If you are not using these and you want to average gradients, you should use
  `tf.math.reduce_sum` to add up your per-example losses and then divide by the
  global batch size. Note that when using `tf.distribute.Strategy`, the first
  component of a tensor's shape is the *replica-local* batch size, which is off
  by a factor equal to the number of replicas being used to compute a single
  step. As a result, using `tf.math.reduce_mean` will give the wrong answer,
  resulting in gradients that can be many times too big.

  ### Variable Constraints

  All Keras optimizers respect variable constraints. If constraint function is
  passed to any variable, the constraint will be applied to the variable after
  the gradient has been applied to the variable.
  Important: If gradient is sparse tensor, variable constraint is not supported.

  ### Thread Compatibility

  The entire optimizer is currently thread compatible, not thread-safe. The user
  needs to perform synchronization if necessary.

  ### Slots

  Many optimizer subclasses, such as `Adam` and `Adagrad` allocate and manage
  additional variables associated with the variables to train.  These are called
  <i>Slots</i>.  Slots have names and you can ask the optimizer for the names of
  the slots that it uses.  Once you have a slot name you can ask the optimizer
  for the variable it created to hold the slot value.

  This can be useful if you want to log debug a training algorithm, report stats
  about the slots, etc.

  ### Hyperparameters

  These are arguments passed to the optimizer subclass constructor
  (the `__init__` method), and then passed to `self._set_hyper()`.
  They can be either regular Python values (like 1.0), tensors, or
  callables. If they are callable, the callable will be called during
  `apply_gradients()` to get the value for the hyper parameter.

  Hyperparameters can be overwritten through user code:

  Example:

  ```python
  # Create an optimizer with the desired parameters.
  opt = tf.keras.optimizers.SGD(learning_rate=0.1)
  # `loss` is a callable that takes no argument and returns the value
  # to minimize.
  loss = lambda: 3 * var1 + 2 * var2
  # In eager mode, simply call minimize to update the list of variables.
  opt.minimize(loss, var_list=[var1, var2])
  # update learning rate
  opt.learning_rate = 0.05
  opt.minimize(loss, var_list=[var1, var2])
  ```

  ### Callable learning rate

  Optimizer accepts a callable learning rate in two ways. The first way is
  through built-in or customized
  `tf.keras.optimizers.schedules.LearningRateSchedule`. The schedule will be
  called on each iteration with `schedule(iteration)`, a `tf.Variable`
  owned by the optimizer.

  Example:

  >>> var = tf.Variable(np.random.random(size=(1,)))
  >>> learning_rate = tf.keras.optimizers.schedules.ExponentialDecay(
  ... initial_learning_rate=.01, decay_steps=20, decay_rate=.1)
  >>> opt = tf.keras.optimizers.SGD(learning_rate=learning_rate)
  >>> loss = lambda: 3 * var
  >>> opt.minimize(loss, var_list=[var])
  <tf.Variable...

  The second way is through a callable function that
  does not accept any arguments.

  Example:

  >>> var = tf.Variable(np.random.random(size=(1,)))
  >>> def lr_callable():
  ...   return .1
  >>> opt = tf.keras.optimizers.SGD(learning_rate=lr_callable)
  >>> loss = lambda: 3 * var
  >>> opt.minimize(loss, var_list=[var])
  <tf.Variable...

  ### Creating a custom optimizer

  If you intend to create your own optimization algorithm, simply inherit from
  this class and override the following methods:

    - `_resource_apply_dense` (update variable given gradient tensor is a dense
      `tf.Tensor`)
    - `_resource_apply_sparse` (update variable given gradient tensor is a
      sparse `tf.IndexedSlices`. The most common way for this to happen
      is if you are taking the gradient through a `tf.gather`.)
    - `_create_slots`
      (if your optimizer algorithm requires additional variables)
    - `get_config`
      (serialization of the optimizer, include all hyper parameters)
  """

  # Subclasses should set this to True unless they override `apply_gradients`
  # with a version that does not have the `experimental_aggregate_gradients`
  # argument.  Older versions of Keras did not have this argument so custom
  # optimizers may have overridden `apply_gradients` without the
  # `experimental_aggregate_gradients` argument. Keras only passes
  # `experimental_aggregate_gradients` if this attribute is True.
  # Note: This attribute will likely be removed in an upcoming release.
  _HAS_AGGREGATE_GRAD = False

  def __init__(self,
               name,
               gradient_aggregator=None,
               gradient_transformers=None,
               **kwargs):
    """Create a new Optimizer.

    This must be called by the constructors of subclasses.
    Note that Optimizer instances should not bind to a single graph,
    and so shouldn't keep Tensors as member variables. Generally
    you should be able to use the _set_hyper()/state.get_hyper()
    facility instead.

    This class is stateful and thread-compatible.

    Example of custom gradient transformations:

    ```python
    def my_gradient_transformer(grads_and_vars):
      # Simple example, double the gradients.
      return [(2. * g, v) for g, v in grads_and_vars]

    optimizer = tf.keras.optimizers.SGD(
        1e-3, gradient_transformers=[my_gradient_transformer])
    ```

    Args:
      name: String. The name to use for momentum accumulator weights created
        by the optimizer.
      gradient_aggregator: The function to use to aggregate gradients across
        devices (when using `tf.distribute.Strategy`). If `None`, defaults to
        summing the gradients across devices. The function should accept and
        return a list of `(gradient, variable)` tuples.
      gradient_transformers: Optional. List of functions to use to transform
        gradients before applying updates to Variables. The functions are
        applied after `gradient_aggregator`. The functions should accept and
        return a list of `(gradient, variable)` tuples.
      **kwargs: keyword arguments. Allowed arguments are `clipvalue`,
        `clipnorm`, `global_clipnorm`.
        If `clipvalue` (float) is set, the gradient of each weight
        is clipped to be no higher than this value.
        If `clipnorm` (float) is set, the gradient of each weight
        is individually clipped so that its norm is no higher than this value.
        If `global_clipnorm` (float) is set the gradient of all weights is
        clipped so that their global norm is no higher than this value.

    Raises:
      ValueError: in case of any invalid argument.
    """
    # Instrument optimizer usages
    keras_optimizers_gauge.get_cell(self.__class__.__name__).set(True)

    allowed_kwargs = {"clipnorm", "clipvalue", "lr", "decay", "global_clipnorm"}
    for k in kwargs:
      if k not in allowed_kwargs:
        raise TypeError("Unexpected keyword argument "
                        "passed to optimizer: " + str(k))
      # checks that all keyword arguments are non-negative.
      if kwargs[k] is not None and kwargs[k] < 0:
        raise ValueError("Expected {} >= 0, received: {}".format(k, kwargs[k]))
      if k == "lr":
        warnings.warn(
            "The `lr` argument is deprecated, use `learning_rate` instead.")

    self._use_locking = True
    self._init_set_name(name)
    self._hyper = {}
    # dict: {variable name : {slot name : variable}}
    self._slots = {}
    self._slot_names = []
    self._weights = []
    self._iterations = None

    # For implementing Trackable. Stores information about how to restore
    # slot variables which have not yet been created
    # (trackable._CheckpointPosition objects).
    #  {slot_name :
    #      {_var_key(variable_to_train): [checkpoint_position, ... ], ... },
    #   ... }
    self._deferred_slot_restorations = {}

    decay = kwargs.pop("decay", 0.0)
    if decay < 0.:
      raise ValueError("decay cannot be less than 0: {}".format(decay))
    self._initial_decay = decay

    self._hypers_created = False
    # Store the distribution strategy object if the optimizer is created inside
    # strategy scope, so it could be used to create variables later.
    if tf.distribute.has_strategy():
      self._distribution_strategy = tf.distribute.get_strategy()
    else:
      self._distribution_strategy = None

    # Configure gradient transformations.
    if gradient_aggregator is None:
      gradient_aggregator = optimizer_utils.all_reduce_sum_gradients
    self.gradient_aggregator = gradient_aggregator
    if gradient_transformers is None:
      gradient_transformers = []
    self.gradient_transformers = gradient_transformers
    self.clipnorm = kwargs.pop("clipnorm", None)
    self.global_clipnorm = kwargs.pop("global_clipnorm", None)
    if self.clipnorm is not None and self.global_clipnorm is not None:
      raise ValueError("Cannot accept both `clipnorm` and `global_clipnorm`, "
                       "passed `clipnorm` {}, `global_clipnorm` {}".format(
                           self.clipnorm, self.global_clipnorm))
    self.clipvalue = kwargs.pop("clipvalue", None)

  @property
  def clipnorm(self):
    """`float` or `None`. If set, clips gradients to a maximum norm."""
    return self._clipnorm

  @property
  def global_clipnorm(self):
    """`float` or `None`. If set, clips gradients to a maximum norm."""
    return self._global_clipnorm

  @clipnorm.setter
  def clipnorm(self, val):
    if val is not None and self.gradient_transformers:
      raise ValueError("`clipnorm` cannot be set when `gradient_transformers` "
                       "is set. Instead, use the `gradient_transformers` to "
                       "specify clipping and other transformations.")
    self._clipnorm = val
    self._clipnorm_fn = optimizer_utils.make_gradient_clipnorm_fn(
        self._clipnorm)

  @global_clipnorm.setter
  def global_clipnorm(self, val):
    if val is not None and self.gradient_transformers:
      raise ValueError("`clipnorm` cannot be set when `gradient_transformers` "
                       "is set. Instead, use the `gradient_transformers` to "
                       "specify clipping and other transformations.")
    self._global_clipnorm = val
    self._global_clipnorm_fn = optimizer_utils.make_global_gradient_clipnorm_fn(
        self._global_clipnorm)

  @property
  def clipvalue(self):
    """`float` or `None`. If set, clips gradients to a maximum value."""
    return self._clipvalue

  @clipvalue.setter
  def clipvalue(self, val):
    if val is not None and self.gradient_transformers:
      raise ValueError("`clipvalue` cannot be set when `gradient_transformers` "
                       "is set. Instead, use the `gradient_transformers` to "
                       "specify clipping and other transformations.")
    self._clipvalue = val
    self._clipvalue_fn = optimizer_utils.make_gradient_clipvalue_fn(
        self._clipvalue)

  def _transform_loss(self, loss):
    """Called in `.minimize` to transform loss before computing gradients."""
    return loss

  def _get_gradients(self, tape, loss, var_list, grad_loss=None):
    """Called in `minimize` to compute gradients from loss."""
    grads = tape.gradient(loss, var_list, grad_loss)
    return list(zip(grads, var_list))

  def _transform_unaggregated_gradients(self, grads_and_vars):
    """Called in `apply_gradients` before gradient aggregation."""
    return grads_and_vars

  def _aggregate_gradients(self, grads_and_vars):
    """Called in `apply_gradients` to aggregate gradients across devices.

    Note that user subclasses may override this, so the interface should not be
    changed.

    Args:
      grads_and_vars: List of (gradient, variable) pairs.

    Returns:
      A list of (aggregrated_gradient, variable) pairs. By default, this calls
      `self.gradient_aggregator`.
    """
    return self.gradient_aggregator(grads_and_vars)

  def _transform_gradients(self, grads_and_vars):
    """Called in `apply_gradients` after aggregation."""
    if self._clipvalue is not None:
      grads_and_vars = self._clipvalue_fn(grads_and_vars)
    if self._clipnorm is not None:
      grads_and_vars = self._clipnorm_fn(grads_and_vars)
    if self._global_clipnorm is not None:
      grads_and_vars = self._global_clipnorm_fn(grads_and_vars)

    for fn in self.gradient_transformers:
      grads_and_vars = fn(grads_and_vars)
    return grads_and_vars

  def minimize(self, loss, var_list, grad_loss=None, name=None, tape=None):
    """Minimize `loss` by updating `var_list`.

    This method simply computes gradient using `tf.GradientTape` and calls
    `apply_gradients()`. If you want to process the gradient before applying
    then call `tf.GradientTape` and `apply_gradients()` explicitly instead
    of using this function.

    Args:
      loss: `Tensor` or callable. If a callable, `loss` should take no arguments
        and return the value to minimize. If a `Tensor`, the `tape` argument
        must be passed.
      var_list: list or tuple of `Variable` objects to update to minimize
        `loss`, or a callable returning the list or tuple of `Variable` objects.
        Use callable when the variable list would otherwise be incomplete before
        `minimize` since the variables are created at the first time `loss` is
        called.
      grad_loss: (Optional). A `Tensor` holding the gradient computed for
        `loss`.
      name: (Optional) str. Name for the returned operation.
      tape: (Optional) `tf.GradientTape`. If `loss` is provided as a `Tensor`,
        the tape that computed the `loss` must be provided.

    Returns:
      An `Operation` that updates the variables in `var_list`. The `iterations`
      will be automatically increased by 1.

    Raises:
      ValueError: If some of the variables are not `Variable` objects.

    """
    grads_and_vars = self._compute_gradients(
        loss, var_list=var_list, grad_loss=grad_loss, tape=tape)
    return self.apply_gradients(grads_and_vars, name=name)

  def _compute_gradients(self, loss, var_list, grad_loss=None, tape=None):
    """Compute gradients of `loss` for the variables in `var_list`.

    This is the first part of `minimize()`.  It returns a list
    of (gradient, variable) pairs where "gradient" is the gradient
    for "variable".  Note that "gradient" can be a `Tensor`, an
    `IndexedSlices`, or `None` if there is no gradient for the
    given variable.

    Args:
      loss: `Tensor` or callable. If a callable, `loss` should take no
        arguments and return the value to minimize. If a `Tensor`, the `tape`
        argument must be passed.
      var_list: list or tuple of `Variable` objects to update to minimize
        `loss`, or a callable returning the list or tuple of `Variable` objects.
        Use callable when the variable list would otherwise be incomplete before
        `minimize` and the variables are created at the first time when `loss`
        is called.
      grad_loss: Optional. A `Tensor` holding the gradient computed for `loss`.
      tape: (Optional) `tf.GradientTape`. If `loss` is provided as a `Tensor`,
        the tape that computed the `loss` must be provided.

    Returns:
      A list of (gradient, variable) pairs. Variable is always present, but
      gradient can be `None`.

    Raises:
      TypeError: If `var_list` contains anything else than `Variable` objects.
      ValueError: If some arguments are invalid, or var_list is None.
    """
    # TODO(joshl): Test that we handle weight decay in a reasonable way.
    if not callable(loss) and tape is None:
      raise ValueError("`tape` is required when a `Tensor` loss is passed.")
    tape = tape if tape is not None else tf.GradientTape()

    if callable(loss):
      with tape:
        if not callable(var_list):
          tape.watch(var_list)
        loss = loss()
        if callable(var_list):
          var_list = var_list()

    with tape:
      loss = self._transform_loss(loss)

    var_list = tf.nest.flatten(var_list)
    with tf.name_scope(self._name + "/gradients"):
      grads_and_vars = self._get_gradients(tape, loss, var_list, grad_loss)

    self._assert_valid_dtypes([
        v for g, v in grads_and_vars
        if g is not None and v.dtype != tf.resource
    ])

    return grads_and_vars

  def apply_gradients(self,
                      grads_and_vars,
                      name=None,
                      experimental_aggregate_gradients=True):
    """Apply gradients to variables.

    This is the second part of `minimize()`. It returns an `Operation` that
    applies gradients.

    The method sums gradients from all replicas in the presence of
    `tf.distribute.Strategy` by default. You can aggregate gradients yourself by
    passing `experimental_aggregate_gradients=False`.

    Example:

    ```python
    grads = tape.gradient(loss, vars)
    grads = tf.distribute.get_replica_context().all_reduce('sum', grads)
    # Processing aggregated gradients.
    optimizer.apply_gradients(zip(grads, vars),
        experimental_aggregate_gradients=False)

    ```

    Args:
      grads_and_vars: List of (gradient, variable) pairs.
      name: Optional name for the returned operation. Default to the name passed
        to the `Optimizer` constructor.
      experimental_aggregate_gradients: Whether to sum gradients from different
        replicas in the presense of `tf.distribute.Strategy`. If False, it's
        user responsibility to aggregate the gradients. Default to True.

    Returns:
      An `Operation` that applies the specified gradients. The `iterations`
      will be automatically increased by 1.

    Raises:
      TypeError: If `grads_and_vars` is malformed.
      ValueError: If none of the variables have gradients.
      RuntimeError: If called in a cross-replica context.
    """
    grads_and_vars = optimizer_utils.filter_empty_gradients(grads_and_vars)
    var_list = [v for (_, v) in grads_and_vars]

    with tf.name_scope(self._name):
      # Create iteration if necessary.
      with tf.init_scope():
        self._create_all_weights(var_list)

      if not grads_and_vars:
        # Distribution strategy does not support reducing an empty list of
        # gradients
        return tf.no_op()

      if tf.distribute.in_cross_replica_context():
        raise RuntimeError(
            "`apply_gradients() cannot be called in cross-replica context. "
            "Use `tf.distribute.Strategy.run` to enter replica "
            "context.")

      strategy = tf.distribute.get_strategy()
      if (not experimental_aggregate_gradients and strategy and
          isinstance(strategy,
                     (tf.compat.v1.distribute.experimental.ParameterServerStrategy,
                      tf.distribute.experimental.ParameterServerStrategy,
                      tf.distribute.experimental.CentralStorageStrategy,
                      tf.compat.v1.distribute.experimental.CentralStorageStrategy))):
        raise NotImplementedError(
            "`experimental_aggregate_gradients=False is not supported for "
            "ParameterServerStrategy and CentralStorageStrategy")

      apply_state = self._prepare(var_list)
      if experimental_aggregate_gradients:
        grads_and_vars = self._transform_unaggregated_gradients(grads_and_vars)
        grads_and_vars = self._aggregate_gradients(grads_and_vars)
      grads_and_vars = self._transform_gradients(grads_and_vars)

      if optimizer_utils.strategy_supports_no_merge_call():
        return self._distributed_apply(strategy, grads_and_vars, name,
                                       apply_state)
      else:
        return tf.distribute.get_replica_context().merge_call(
            functools.partial(self._distributed_apply, apply_state=apply_state),
            args=(grads_and_vars,),
            kwargs={
                "name": name,
            })

  def _distributed_apply(self, distribution, grads_and_vars, name, apply_state):
    """`apply_gradients` using a `DistributionStrategy`."""

    def apply_grad_to_update_var(var, grad):
      """Apply gradient to variable."""
      if isinstance(var, tf.Tensor):
        raise NotImplementedError("Trying to update a Tensor ", var)

      apply_kwargs = {}
      if isinstance(grad, tf.IndexedSlices):
        if var.constraint is not None:
          raise RuntimeError(
              "Cannot use a constraint function on a sparse variable.")
        if "apply_state" in self._sparse_apply_args:
          apply_kwargs["apply_state"] = apply_state
        return self._resource_apply_sparse_duplicate_indices(
            grad.values, var, grad.indices, **apply_kwargs)

      if "apply_state" in self._dense_apply_args:
        apply_kwargs["apply_state"] = apply_state
      update_op = self._resource_apply_dense(grad, var, **apply_kwargs)
      if var.constraint is not None:
        with tf.control_dependencies([update_op]):
          return var.assign(var.constraint(var))
      else:
        return update_op

    eagerly_outside_functions = tf.compat.v1.executing_eagerly_outside_functions()
    update_ops = []
    with name_scope_only_in_function_or_graph(name or self._name):
      for grad, var in grads_and_vars:
        # Colocate the update with variables to avoid unnecessary communication
        # delays. See b/136304694.
        with distribution.extended.colocate_vars_with(var):
          with name_scope_only_in_function_or_graph(
              "update" if eagerly_outside_functions else "update_" +
              var.op.name):
            update_op = distribution.extended.update(
                var, apply_grad_to_update_var, args=(grad,), group=False)
            if tf.distribute.in_cross_replica_context():
              # In cross-replica context, extended.update returns a list of
              # update ops from all replicas (group=False).
              update_ops.extend(update_op)
            else:
              # In replica context, extended.update return the single update op
              # of current replica.
              update_ops.append(update_op)

      any_symbolic = any(isinstance(i, tf.Operation) or
                         tf_utils.is_symbolic_tensor(i) for i in update_ops)
      if not tf.executing_eagerly() or any_symbolic:
        # If the current context is graph mode or any of the update ops are
        # symbolic then the step update should be carried out under a graph
        # context. (eager updates execute immediately)
        with backend._current_graph(update_ops).as_default():  # pylint: disable=protected-access
          with tf.control_dependencies([tf.group(update_ops)]):
            return self._iterations.assign_add(1, read_value=False)

      return self._iterations.assign_add(1)

  def get_gradients(self, loss, params):
    """Returns gradients of `loss` with respect to `params`.

    Should be used only in legacy v1 graph mode.

    Args:
      loss: Loss tensor.
      params: List of variables.

    Returns:
      List of gradient tensors.

    Raises:
      ValueError: In case any gradient cannot be computed (e.g. if gradient
        function not implemented).
    """
    params = tf.nest.flatten(params)
    with backend.get_graph().as_default(), backend.name_scope(self._name +
                                                              "/gradients"):
      grads = tf.compat.v1.gradients(loss, params)
      for grad, param in zip(grads, params):
        if grad is None:
          raise ValueError("Variable {} has `None` for gradient. "
                           "Please make sure that all of your ops have a "
                           "gradient defined (i.e. are differentiable). "
                           "Common ops without gradient: "
                           "K.argmax, K.round, K.eval.".format(param))
    return grads

  def get_updates(self, loss, params):
    grads = self.get_gradients(loss, params)
    grads_and_vars = list(zip(grads, params))
    self._assert_valid_dtypes([
        v for g, v in grads_and_vars
        if g is not None and v.dtype != tf.resource
    ])
    return [self.apply_gradients(grads_and_vars)]

  def _set_hyper(self, name, value):
    """set hyper `name` to value. value can be callable, tensor, numeric."""
    if isinstance(value, tf.__internal__.tracking.Trackable):
      self._track_trackable(value, name, overwrite=True)
    if name not in self._hyper:
      self._hyper[name] = value
    else:
      prev_value = self._hyper[name]
      if (callable(prev_value)
          or isinstance(prev_value,
                        (tf.Tensor, int, float,
                         learning_rate_schedule.LearningRateSchedule))
          or isinstance(value, learning_rate_schedule.LearningRateSchedule)):
        self._hyper[name] = value
      else:
        backend.set_value(self._hyper[name], value)

  def _get_hyper(self, name, dtype=None):
    if not self._hypers_created:
      self._create_hypers()
    value = self._hyper[name]
    if isinstance(value, learning_rate_schedule.LearningRateSchedule):
      return value
    if callable(value):
      value = value()
    if dtype:
      return tf.cast(value, dtype)
    else:
      return value

  def _create_slots(self, var_list):
    pass

  def _create_all_weights(self, var_list):
    """Creates all weights, including iterations, hyperparameters and slot vars.

    This will add newly created variables to `optimizer.weights`.

    New variables are only created when this method is called the first time, or
    when called with different variables in the var_list.

    Args:
      var_list: list or tuple of `Variable` objects that will be minimized
        using this optimizer.
    """

    _ = self.iterations
    self._create_hypers()
    self._create_slots(var_list)

  def __getattribute__(self, name):
    """Overridden to support hyperparameter access."""
    try:
      return super(OptimizerV2, self).__getattribute__(name)
    except AttributeError as e:
      # Needed to avoid infinite recursion with __setattr__.
      if name == "_hyper":
        raise e
      # Backwards compatibility with Keras optimizers.
      if name == "lr":
        name = "learning_rate"
      if name in self._hyper:
        return self._get_hyper(name)
      raise e

  def __dir__(self):
    result = set(super(OptimizerV2, self).__dir__())
    if "_hyper" in result:
      result |= self._hyper.keys()
      if "learning_rate" in self._hyper.keys():
        result.add("lr")
    return list(result)

  def __setattr__(self, name, value):
    """Override setattr to support dynamic hyperparameter setting."""
    # Backwards compatibility with Keras optimizers.
    if name == "lr":
      name = "learning_rate"
    if hasattr(self, "_hyper") and name in self._hyper:
      self._set_hyper(name, value)
    else:
      super(OptimizerV2, self).__setattr__(name, value)

  def get_slot_names(self):
    """A list of names for this optimizer's slots."""
    return self._slot_names

  def add_slot(self, var, slot_name, initializer="zeros", shape=None):
    """Add a new slot variable for `var`.

    A slot variable is an additional variable associated with `var` to train.
    It is allocated and managed by optimizers, e.g. `Adam`.

    Args:
      var: a `Variable` object.
      slot_name: name of the slot variable.
      initializer: initializer of the slot variable
      shape: (Optional) shape of the slot variable. If not set, it will default
      to the shape of `var`.

    Returns:
      A slot variable.
    """
    if slot_name not in self._slot_names:
      self._slot_names.append(slot_name)
    var_key = _var_key(var)
    slot_dict = self._slots.setdefault(var_key, {})
    weight = slot_dict.get(slot_name, None)
    if weight is None:
      if isinstance(initializer, str) or callable(initializer):
        initializer = initializers.get(initializer)
        if isinstance(
            initializer,
            tf.__internal__.tracking.CheckpointInitialValueCallable) or (shape is not None):
          slot_shape = shape
        else:
          slot_shape = var.shape
        initial_value = functools.partial(
            initializer, shape=slot_shape, dtype=var.dtype)
      else:
        initial_value = initializer

      with self._distribution_strategy_scope():
        strategy = tf.distribute.get_strategy()
        if not strategy.extended.variable_created_in_scope(var):
          raise ValueError(
              "Trying to create optimizer slot variable under the scope for "
              "tf.distribute.Strategy ({}), which is different from the scope "
              "used for the original variable ({}). Make sure the slot "
              "variables are created under the same strategy scope. This may "
              "happen if you're restoring from a checkpoint outside the scope"
              .format(strategy, var))

        with strategy.extended.colocate_vars_with(var):
          weight = tf.Variable(
              name="%s/%s" % (var._shared_name, slot_name),  # pylint: disable=protected-access
              dtype=var.dtype,
              trainable=False,
              initial_value=initial_value)
      backend.track_variable(weight)
      slot_dict[slot_name] = weight
      self._restore_slot_variable(
          slot_name=slot_name, variable=var,
          slot_variable=weight)
      self._weights.append(weight)
    return weight

  def get_slot(self, var, slot_name):
    var_key = _var_key(var)
    slot_dict = self._slots[var_key]
    return slot_dict[slot_name]

  def _prepare(self, var_list):
    keys = set()
    for var in var_list:
      if isinstance(var, tf.distribute.DistributedValues):
        var_devices = var._devices   # pylint: disable=protected-access
      else:
        var_devices = [var.device]
      var_dtype = var.dtype.base_dtype
      for var_device in var_devices:
        keys.add((var_device, var_dtype))

    apply_state = {}
    for var_device, var_dtype in keys:
      apply_state[(var_device, var_dtype)] = {}
      with tf.device(var_device):
        self._prepare_local(var_device, var_dtype, apply_state)

    return apply_state

  def _prepare_local(self, var_device, var_dtype, apply_state):
    if "learning_rate" in self._hyper:
      lr_t = tf.identity(self._decayed_lr(var_dtype))
      apply_state[(var_device, var_dtype)]["lr_t"] = lr_t

  def _fallback_apply_state(self, var_device, var_dtype):
    """Compatibility for subclasses that don't pass apply_state through."""
    apply_state = {(var_device, var_dtype): {}}
    self._prepare_local(var_device, var_dtype, apply_state)
    return apply_state[(var_device, var_dtype)]

  def _create_hypers(self):
    if self._hypers_created:
      return
    with self._distribution_strategy_scope():
      # Iterate hyper values deterministically.
      for name, value in sorted(self._hyper.items()):
        if isinstance(value,
                      (tf.Tensor, tf.Variable)) or callable(value):
          # The check for `callable` covers the usage when `value` is a
          # `LearningRateSchedule`, in which case it does not need to create a
          # variable.
          continue
        else:
          self._hyper[name] = self.add_weight(
              name,
              shape=[],
              trainable=False,
              initializer=value,
              aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA)
    self._hypers_created = True

  @property
  def iterations(self):
    """Variable. The number of training steps this Optimizer has run."""
    if self._iterations is None:
      with self._distribution_strategy_scope():
        self._iterations = self.add_weight(
            "iter",
            shape=[],
            dtype=tf.int64,
            trainable=False,
            aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA)
      self._weights.append(self._iterations)
    return self._iterations

  @iterations.setter
  def iterations(self, variable):
    if self._iterations is not None:
      raise RuntimeError("Cannot set `iterations` to a new Variable after "
                         "the Optimizer weights have been created")
    self._iterations = variable
    self._weights.append(self._iterations)

  def _decayed_lr(self, var_dtype):
    """Get decayed learning rate as a Tensor with dtype=var_dtype."""
    lr_t = self._get_hyper("learning_rate", var_dtype)
    if isinstance(lr_t, learning_rate_schedule.LearningRateSchedule):
      local_step = tf.cast(self.iterations, var_dtype)
      lr_t = tf.cast(lr_t(local_step), var_dtype)
    if self._initial_decay > 0.:
      local_step = tf.cast(self.iterations, var_dtype)
      decay_t = tf.cast(self._initial_decay, var_dtype)
      lr_t = lr_t / (1. + decay_t * local_step)
    return lr_t

  @abc.abstractmethod
  def get_config(self):
    """Returns the config of the optimizer.

    An optimizer config is a Python dictionary (serializable)
    containing the configuration of an optimizer.
    The same optimizer can be reinstantiated later
    (without any saved state) from this configuration.

    Returns:
        Python dictionary.
    """
    config = {"name": self._name}
    if self.clipnorm is not None:
      config["clipnorm"] = self.clipnorm
    if self.clipvalue is not None:
      config["clipvalue"] = self.clipvalue
    if self.global_clipnorm is not None:
      config["global_clipnorm"] = self.global_clipnorm
    return config

  @classmethod
  def from_config(cls, config, custom_objects=None):
    """Creates an optimizer from its config.

    This method is the reverse of `get_config`,
    capable of instantiating the same optimizer from the config
    dictionary.

    Args:
        config: A Python dictionary, typically the output of get_config.
        custom_objects: A Python dictionary mapping names to additional Python
          objects used to create this optimizer, such as a function used for a
          hyperparameter.

    Returns:
        An optimizer instance.
    """
    if "lr" in config:
      config["learning_rate"] = config.pop("lr")
    if "learning_rate" in config:
      if isinstance(config["learning_rate"], dict):
        config["learning_rate"] = learning_rate_schedule.deserialize(
            config["learning_rate"], custom_objects=custom_objects)
    return cls(**config)

  def _serialize_hyperparameter(self, hyperparameter_name):
    """Serialize a hyperparameter that can be a float, callable, or Tensor."""
    value = self._hyper[hyperparameter_name]
    if isinstance(value, learning_rate_schedule.LearningRateSchedule):
      return learning_rate_schedule.serialize(value)
    if callable(value):
      return value()
    if tf.is_tensor(value):
      return backend.get_value(value)
    return value

  def variables(self):
    """Returns variables of this Optimizer based on the order created."""
    return self._weights

  @property
  def weights(self):
    """Returns variables of this Optimizer based on the order created."""
    return self._weights

  def get_weights(self):
    """Returns the current weights of the optimizer.

    The weights of an optimizer are its state (ie, variables).
    This function returns the weight values associated with this
    optimizer as a list of Numpy arrays. The first value is always the
    iterations count of the optimizer, followed by the optimizer's state
    variables in the order they were created. The returned list can in turn
    be used to load state into similarly parameterized optimizers.

    For example, the RMSprop optimizer for this simple model returns a list of
    three values-- the iteration count, followed by the root-mean-square value
    of the kernel and bias of the single Dense layer:

    >>> opt = tf.keras.optimizers.RMSprop()
    >>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
    >>> m.compile(opt, loss='mse')
    >>> data = np.arange(100).reshape(5, 20)
    >>> labels = np.zeros(5)
    >>> print('Training'); results = m.fit(data, labels)
    Training ...
    >>> len(opt.get_weights())
    3

    Returns:
        Weights values as a list of numpy arrays.
    """
    params = self.weights
    return backend.batch_get_value(params)

  # TODO(tanzheny): Maybe share this logic with base_layer.
  def set_weights(self, weights):
    """Set the weights of the optimizer.

    The weights of an optimizer are its state (ie, variables).
    This function takes the weight values associated with this
    optimizer as a list of Numpy arrays. The first value is always the
    iterations count of the optimizer, followed by the optimizer's state
    variables in the order they are created. The passed values are used to set
    the new state of the optimizer.

    For example, the RMSprop optimizer for this simple model takes a list of
    three values-- the iteration count, followed by the root-mean-square value
    of the kernel and bias of the single Dense layer:

    >>> opt = tf.keras.optimizers.RMSprop()
    >>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
    >>> m.compile(opt, loss='mse')
    >>> data = np.arange(100).reshape(5, 20)
    >>> labels = np.zeros(5)
    >>> print('Training'); results = m.fit(data, labels)
    Training ...
    >>> new_weights = [np.array(10), np.ones([20, 10]), np.zeros([10])]
    >>> opt.set_weights(new_weights)
    >>> opt.iterations
    <tf.Variable 'RMSprop/iter:0' shape=() dtype=int64, numpy=10>

    Args:
        weights: weight values as a list of numpy arrays.
    """
    params = self.weights
    if len(params) != len(weights):
      raise ValueError(
          "You called `set_weights(weights)` on optimizer " + self._name +
          " with a  weight list of length " + str(len(weights)) +
          ", but the optimizer was expecting " + str(len(params)) +
          " weights. Provided weights: " + str(weights)[:50] + "...")
    if not params:
      return
    weight_value_tuples = []
    param_values = backend.batch_get_value(params)
    for pv, p, w in zip(param_values, params, weights):
      if pv.shape != w.shape:
        raise ValueError("Optimizer weight shape " + str(pv.shape) +
                         " not compatible with "
                         "provided weight shape " + str(w.shape))
      weight_value_tuples.append((p, w))
    backend.batch_set_value(weight_value_tuples)

  def add_weight(self,
                 name,
                 shape,
                 dtype=None,
                 initializer="zeros",
                 trainable=None,
                 synchronization=tf.VariableSynchronization.AUTO,
                 aggregation=tf.VariableAggregation.NONE):

    if dtype is None:
      dtype = tf.float32
    if isinstance(initializer, str) or callable(initializer):
      initializer = initializers.get(initializer)

    if synchronization == tf.VariableSynchronization.ON_READ:
      if trainable:
        raise ValueError(
            "Synchronization value can be set to "
            "VariableSynchronization.ON_READ only for non-trainable variables. "
            "You have specified trainable=True and "
            "synchronization=VariableSynchronization.ON_READ.")
      else:
        # Set trainable to be false when variable is to be synced on read.
        trainable = False
    elif trainable is None:
      trainable = True

    variable = self._add_variable_with_custom_getter(
        name=name,
        shape=shape,
        getter=base_layer_utils.make_variable,
        overwrite=True,
        initializer=initializer,
        dtype=dtype,
        trainable=trainable,
        use_resource=True,
        synchronization=synchronization,
        aggregation=aggregation)
    backend.track_variable(variable)

    return variable

  def _init_set_name(self, name, zero_based=True):
    if not name:
      self._name = backend.unique_object_name(
          generic_utils.to_snake_case(self.__class__.__name__),
          zero_based=zero_based)
    else:
      self._name = name

  def _assert_valid_dtypes(self, tensors):
    """Asserts tensors are all valid types (see `_valid_dtypes`).

    Args:
      tensors: Tensors to check.

    Raises:
      ValueError: If any tensor is not a valid type.
    """
    valid_dtypes = self._valid_dtypes()
    for t in tensors:
      dtype = t.dtype.base_dtype
      if dtype not in valid_dtypes:
        raise ValueError("Invalid type %r for %s, expected: %s." %
                         (dtype, t.name, [v for v in valid_dtypes]))

  def _valid_dtypes(self):
    """Valid types for loss, variables and gradients.

    Subclasses should override to allow other float types.

    Returns:
      Valid types for loss, variables and gradients.
    """
    return _DEFAULT_VALID_DTYPES

  def _call_if_callable(self, param):
    """Call the function if param is callable."""
    return param() if callable(param) else param

  def _resource_apply_dense(self, grad, handle, apply_state):
    """Add ops to apply dense gradients to the variable `handle`.

    Args:
      grad: a `Tensor` representing the gradient.
      handle: a `Tensor` of dtype `resource` which points to the variable to be
        updated.
      apply_state: A dict which is used across multiple apply calls.

    Returns:
      An `Operation` which updates the value of the variable.
    """
    raise NotImplementedError("Must be implemented in subclasses.")

  def _resource_apply_sparse_duplicate_indices(self, grad, handle, indices,
                                               **kwargs):
    """Add ops to apply sparse gradients to `handle`, with repeated indices.

    Optimizers which override this method must deal with repeated indices. See
    the docstring of `_apply_sparse_duplicate_indices` for details. By default
    the correct behavior, to sum non-unique indices and their associated
    gradients, is enforced by first pre-processing `grad` and `indices` and
    passing them on to `_resource_apply_sparse`. Optimizers which deal correctly
    with duplicate indices may instead override this method to avoid the
    overhead of summing.

    Args:
      grad: a `Tensor` representing the gradient for the affected indices.
      handle: a `Tensor` of dtype `resource` which points to the variable to be
        updated.
      indices: a `Tensor` of integral type representing the indices for which
        the gradient is nonzero. Indices may be repeated.
      **kwargs: May optionally contain `apply_state`

    Returns:
      An `Operation` which updates the value of the variable.
    """
    summed_grad, unique_indices = _deduplicate_indexed_slices(
        values=grad, indices=indices)
    return self._resource_apply_sparse(summed_grad, handle, unique_indices,
                                       **kwargs)

  def _resource_apply_sparse(self, grad, handle, indices, apply_state):
    """Add ops to apply sparse gradients to the variable `handle`.

    Similar to `_apply_sparse`, the `indices` argument to this method has been
    de-duplicated. Optimizers which deal correctly with non-unique indices may
    instead override `_resource_apply_sparse_duplicate_indices` to avoid this
    overhead.

    Args:
      grad: a `Tensor` representing the gradient for the affected indices.
      handle: a `Tensor` of dtype `resource` which points to the variable to be
        updated.
      indices: a `Tensor` of integral type representing the indices for which
        the gradient is nonzero. Indices are unique.
      apply_state: A dict which is used across multiple apply calls.

    Returns:
      An `Operation` which updates the value of the variable.
    """
    raise NotImplementedError("Must be implemented in subclasses.")

  def _resource_scatter_add(self, x, i, v):
    with tf.control_dependencies([
        tf.raw_ops.ResourceScatterAdd(
            resource=x.handle, indices=i, updates=v)
    ]):
      return x.value()

  def _resource_scatter_update(self, x, i, v):
    with tf.control_dependencies(
        [tf.raw_ops.ResourceScatterUpdate(
            resource=x.handle, indices=i, updates=v)]):
      return x.value()

  @property
  @layer_utils.cached_per_instance
  def _dense_apply_args(self):
    return tf_inspect.getfullargspec(self._resource_apply_dense).args

  @property
  @layer_utils.cached_per_instance
  def _sparse_apply_args(self):
    return tf_inspect.getfullargspec(self._resource_apply_sparse).args

  # ---------------
  # For implementing the trackable interface
  # ---------------

  def _restore_slot_variable(self, slot_name, variable, slot_variable):
    """Restore a newly created slot variable's value."""
    variable_key = _var_key(variable)
    deferred_restorations = self._deferred_slot_restorations.get(
        slot_name, {}).pop(variable_key, [])
    # Iterate over restores, highest restore UID first to minimize the number
    # of assignments.
    deferred_restorations.sort(key=lambda position: position.restore_uid,
                               reverse=True)
    for checkpoint_position in deferred_restorations:
      checkpoint_position.restore(slot_variable)

  def _create_or_restore_slot_variable(
      self, slot_variable_position, slot_name, variable):
    """Restore a slot variable's value, possibly creating it.

    Called when a variable which has an associated slot variable is created or
    restored. When executing eagerly, we create the slot variable with a
    restoring initializer.

    No new variables are created when graph building. Instead,
    _restore_slot_variable catches these after normal creation and adds restore
    ops to the graph. This method is nonetheless important when graph building
    for the case when a slot variable has already been created but `variable`
    has just been added to a dependency graph (causing us to realize that the
    slot variable needs to be restored).

    Args:
      slot_variable_position: A `trackable._CheckpointPosition` object
        indicating the slot variable `Trackable` object to be restored.
      slot_name: The name of this `Optimizer`'s slot to restore into.
      variable: The variable object this slot is being created for.
    """
    variable_key = _var_key(variable)
    slot_dict = self._slots.get(variable_key, {})
    slot_variable = slot_dict.get(slot_name, None)
    if (slot_variable is None and tf.executing_eagerly() and
        slot_variable_position.is_simple_variable()
        # Defer slot variable creation if there is an active variable creator
        # scope. Generally we'd like to eagerly create/restore slot variables
        # when possible, but this may mean that scopes intended to catch
        # `variable` also catch its eagerly created slot variable
        # unintentionally (specifically make_template would add a dependency on
        # a slot variable if not for this case). Deferring is mostly harmless
        # (aside from double initialization), and makes variable creator scopes
        # behave the same way they do when graph building.
        #
        # One notable case is with distribution strategy, which uses variable
        # creator scope but always desires the `variable` and the slot to use
        # the same scope, thus we can safely eagerly create/restore slot
        # variables.
        and (not tf.compat.v1.get_default_graph()._variable_creator_stack or  # pylint: disable=protected-access
             self._distribution_strategy)):
      initializer = tf.__internal__.tracking.CheckpointInitialValueCallable(
          checkpoint_position=slot_variable_position)
      slot_variable = self.add_slot(
          var=variable,
          initializer=initializer,
          slot_name=slot_name,
          shape=slot_variable_position.value_shape())
      # Slot variables are not owned by any one object (because we don't want to
      # save the slot variable if the optimizer is saved without the non-slot
      # variable, or if the non-slot variable is saved without the optimizer;
      # it's a dependency hypergraph with edges of the form (optimizer, non-slot
      # variable, variable)). So we don't _track_ slot variables anywhere, and
      # instead special-case this dependency and otherwise pretend it's a normal
      # graph.
    if slot_variable is not None:
      # If we've either made this slot variable, or if we've pulled out an
      # existing slot variable, we should restore it.
      slot_variable_position.restore(slot_variable)
    else:
      # We didn't make the slot variable. Defer restoring until it gets created
      # normally. We keep a list rather than the one with the highest restore
      # UID in case slot variables have their own dependencies, in which case
      # those could differ between restores.
      self._deferred_slot_restorations.setdefault(
          slot_name, {}).setdefault(variable_key, []).append(
              slot_variable_position)

  @contextlib.contextmanager
  def _distribution_strategy_scope(self):
    """Returns the `tf.distribute.Strategy` this optimizer was created under."""
    if self._distribution_strategy and not tf.distribute.has_strategy():
      with self._distribution_strategy.scope():
        yield self._distribution_strategy.scope()
    else:
      yield

Ancestors

  • tensorflow.python.training.tracking.base.Trackable

Subclasses

Static methods

def from_config(config, custom_objects=None)

Creates an optimizer from its config.

This method is the reverse of get_config, capable of instantiating the same optimizer from the config dictionary.

Args

config
A Python dictionary, typically the output of get_config.
custom_objects
A Python dictionary mapping names to additional Python objects used to create this optimizer, such as a function used for a hyperparameter.

Returns

An optimizer instance.

Expand source code
@classmethod
def from_config(cls, config, custom_objects=None):
  """Creates an optimizer from its config.

  This method is the reverse of `get_config`,
  capable of instantiating the same optimizer from the config
  dictionary.

  Args:
      config: A Python dictionary, typically the output of get_config.
      custom_objects: A Python dictionary mapping names to additional Python
        objects used to create this optimizer, such as a function used for a
        hyperparameter.

  Returns:
      An optimizer instance.
  """
  if "lr" in config:
    config["learning_rate"] = config.pop("lr")
  if "learning_rate" in config:
    if isinstance(config["learning_rate"], dict):
      config["learning_rate"] = learning_rate_schedule.deserialize(
          config["learning_rate"], custom_objects=custom_objects)
  return cls(**config)

Instance variables

var clipnorm

float or None. If set, clips gradients to a maximum norm.

Expand source code
@property
def clipnorm(self):
  """`float` or `None`. If set, clips gradients to a maximum norm."""
  return self._clipnorm
var clipvalue

float or None. If set, clips gradients to a maximum value.

Expand source code
@property
def clipvalue(self):
  """`float` or `None`. If set, clips gradients to a maximum value."""
  return self._clipvalue
var global_clipnorm

float or None. If set, clips gradients to a maximum norm.

Expand source code
@property
def global_clipnorm(self):
  """`float` or `None`. If set, clips gradients to a maximum norm."""
  return self._global_clipnorm
var iterations

Variable. The number of training steps this Optimizer has run.

Expand source code
@property
def iterations(self):
  """Variable. The number of training steps this Optimizer has run."""
  if self._iterations is None:
    with self._distribution_strategy_scope():
      self._iterations = self.add_weight(
          "iter",
          shape=[],
          dtype=tf.int64,
          trainable=False,
          aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA)
    self._weights.append(self._iterations)
  return self._iterations
var weights

Returns variables of this Optimizer based on the order created.

Expand source code
@property
def weights(self):
  """Returns variables of this Optimizer based on the order created."""
  return self._weights

Methods

def add_slot(self, var, slot_name, initializer='zeros', shape=None)

Add a new slot variable for var.

A slot variable is an additional variable associated with var to train. It is allocated and managed by optimizers, e.g. Adam.

Args

var
a Variable object.
slot_name
name of the slot variable.
initializer
initializer of the slot variable
shape
(Optional) shape of the slot variable. If not set, it will default

to the shape of var.

Returns

A slot variable.

Expand source code
def add_slot(self, var, slot_name, initializer="zeros", shape=None):
  """Add a new slot variable for `var`.

  A slot variable is an additional variable associated with `var` to train.
  It is allocated and managed by optimizers, e.g. `Adam`.

  Args:
    var: a `Variable` object.
    slot_name: name of the slot variable.
    initializer: initializer of the slot variable
    shape: (Optional) shape of the slot variable. If not set, it will default
    to the shape of `var`.

  Returns:
    A slot variable.
  """
  if slot_name not in self._slot_names:
    self._slot_names.append(slot_name)
  var_key = _var_key(var)
  slot_dict = self._slots.setdefault(var_key, {})
  weight = slot_dict.get(slot_name, None)
  if weight is None:
    if isinstance(initializer, str) or callable(initializer):
      initializer = initializers.get(initializer)
      if isinstance(
          initializer,
          tf.__internal__.tracking.CheckpointInitialValueCallable) or (shape is not None):
        slot_shape = shape
      else:
        slot_shape = var.shape
      initial_value = functools.partial(
          initializer, shape=slot_shape, dtype=var.dtype)
    else:
      initial_value = initializer

    with self._distribution_strategy_scope():
      strategy = tf.distribute.get_strategy()
      if not strategy.extended.variable_created_in_scope(var):
        raise ValueError(
            "Trying to create optimizer slot variable under the scope for "
            "tf.distribute.Strategy ({}), which is different from the scope "
            "used for the original variable ({}). Make sure the slot "
            "variables are created under the same strategy scope. This may "
            "happen if you're restoring from a checkpoint outside the scope"
            .format(strategy, var))

      with strategy.extended.colocate_vars_with(var):
        weight = tf.Variable(
            name="%s/%s" % (var._shared_name, slot_name),  # pylint: disable=protected-access
            dtype=var.dtype,
            trainable=False,
            initial_value=initial_value)
    backend.track_variable(weight)
    slot_dict[slot_name] = weight
    self._restore_slot_variable(
        slot_name=slot_name, variable=var,
        slot_variable=weight)
    self._weights.append(weight)
  return weight
def add_weight(self, name, shape, dtype=None, initializer='zeros', trainable=None, synchronization=VariableSynchronization.AUTO, aggregation=VariableAggregationV2.NONE)
Expand source code
def add_weight(self,
               name,
               shape,
               dtype=None,
               initializer="zeros",
               trainable=None,
               synchronization=tf.VariableSynchronization.AUTO,
               aggregation=tf.VariableAggregation.NONE):

  if dtype is None:
    dtype = tf.float32
  if isinstance(initializer, str) or callable(initializer):
    initializer = initializers.get(initializer)

  if synchronization == tf.VariableSynchronization.ON_READ:
    if trainable:
      raise ValueError(
          "Synchronization value can be set to "
          "VariableSynchronization.ON_READ only for non-trainable variables. "
          "You have specified trainable=True and "
          "synchronization=VariableSynchronization.ON_READ.")
    else:
      # Set trainable to be false when variable is to be synced on read.
      trainable = False
  elif trainable is None:
    trainable = True

  variable = self._add_variable_with_custom_getter(
      name=name,
      shape=shape,
      getter=base_layer_utils.make_variable,
      overwrite=True,
      initializer=initializer,
      dtype=dtype,
      trainable=trainable,
      use_resource=True,
      synchronization=synchronization,
      aggregation=aggregation)
  backend.track_variable(variable)

  return variable
def apply_gradients(self, grads_and_vars, name=None, experimental_aggregate_gradients=True)

Apply gradients to variables.

This is the second part of minimize(). It returns an Operation that applies gradients.

The method sums gradients from all replicas in the presence of tf.distribute.Strategy by default. You can aggregate gradients yourself by passing experimental_aggregate_gradients=False.

Example:

grads = tape.gradient(loss, vars)
grads = tf.distribute.get_replica_context().all_reduce('sum', grads)
# Processing aggregated gradients.
optimizer.apply_gradients(zip(grads, vars),
    experimental_aggregate_gradients=False)

Args

grads_and_vars
List of (gradient, variable) pairs.
name
Optional name for the returned operation. Default to the name passed to the OptimizerV2 constructor.
experimental_aggregate_gradients
Whether to sum gradients from different replicas in the presense of tf.distribute.Strategy. If False, it's user responsibility to aggregate the gradients. Default to True.

Returns

An Operation that applies the specified gradients. The iterations will be automatically increased by 1.

Raises

TypeError
If grads_and_vars is malformed.
ValueError
If none of the variables have gradients.
RuntimeError
If called in a cross-replica context.
Expand source code
def apply_gradients(self,
                    grads_and_vars,
                    name=None,
                    experimental_aggregate_gradients=True):
  """Apply gradients to variables.

  This is the second part of `minimize()`. It returns an `Operation` that
  applies gradients.

  The method sums gradients from all replicas in the presence of
  `tf.distribute.Strategy` by default. You can aggregate gradients yourself by
  passing `experimental_aggregate_gradients=False`.

  Example:

  ```python
  grads = tape.gradient(loss, vars)
  grads = tf.distribute.get_replica_context().all_reduce('sum', grads)
  # Processing aggregated gradients.
  optimizer.apply_gradients(zip(grads, vars),
      experimental_aggregate_gradients=False)

  ```

  Args:
    grads_and_vars: List of (gradient, variable) pairs.
    name: Optional name for the returned operation. Default to the name passed
      to the `Optimizer` constructor.
    experimental_aggregate_gradients: Whether to sum gradients from different
      replicas in the presense of `tf.distribute.Strategy`. If False, it's
      user responsibility to aggregate the gradients. Default to True.

  Returns:
    An `Operation` that applies the specified gradients. The `iterations`
    will be automatically increased by 1.

  Raises:
    TypeError: If `grads_and_vars` is malformed.
    ValueError: If none of the variables have gradients.
    RuntimeError: If called in a cross-replica context.
  """
  grads_and_vars = optimizer_utils.filter_empty_gradients(grads_and_vars)
  var_list = [v for (_, v) in grads_and_vars]

  with tf.name_scope(self._name):
    # Create iteration if necessary.
    with tf.init_scope():
      self._create_all_weights(var_list)

    if not grads_and_vars:
      # Distribution strategy does not support reducing an empty list of
      # gradients
      return tf.no_op()

    if tf.distribute.in_cross_replica_context():
      raise RuntimeError(
          "`apply_gradients() cannot be called in cross-replica context. "
          "Use `tf.distribute.Strategy.run` to enter replica "
          "context.")

    strategy = tf.distribute.get_strategy()
    if (not experimental_aggregate_gradients and strategy and
        isinstance(strategy,
                   (tf.compat.v1.distribute.experimental.ParameterServerStrategy,
                    tf.distribute.experimental.ParameterServerStrategy,
                    tf.distribute.experimental.CentralStorageStrategy,
                    tf.compat.v1.distribute.experimental.CentralStorageStrategy))):
      raise NotImplementedError(
          "`experimental_aggregate_gradients=False is not supported for "
          "ParameterServerStrategy and CentralStorageStrategy")

    apply_state = self._prepare(var_list)
    if experimental_aggregate_gradients:
      grads_and_vars = self._transform_unaggregated_gradients(grads_and_vars)
      grads_and_vars = self._aggregate_gradients(grads_and_vars)
    grads_and_vars = self._transform_gradients(grads_and_vars)

    if optimizer_utils.strategy_supports_no_merge_call():
      return self._distributed_apply(strategy, grads_and_vars, name,
                                     apply_state)
    else:
      return tf.distribute.get_replica_context().merge_call(
          functools.partial(self._distributed_apply, apply_state=apply_state),
          args=(grads_and_vars,),
          kwargs={
              "name": name,
          })
def get_config(self)

Returns the config of the optimizer.

An optimizer config is a Python dictionary (serializable) containing the configuration of an optimizer. The same optimizer can be reinstantiated later (without any saved state) from this configuration.

Returns

Python dictionary.

Expand source code
@abc.abstractmethod
def get_config(self):
  """Returns the config of the optimizer.

  An optimizer config is a Python dictionary (serializable)
  containing the configuration of an optimizer.
  The same optimizer can be reinstantiated later
  (without any saved state) from this configuration.

  Returns:
      Python dictionary.
  """
  config = {"name": self._name}
  if self.clipnorm is not None:
    config["clipnorm"] = self.clipnorm
  if self.clipvalue is not None:
    config["clipvalue"] = self.clipvalue
  if self.global_clipnorm is not None:
    config["global_clipnorm"] = self.global_clipnorm
  return config
def get_gradients(self, loss, params)

Returns gradients of loss with respect to params.

Should be used only in legacy v1 graph mode.

Args

loss
Loss tensor.
params
List of variables.

Returns

List of gradient tensors.

Raises

ValueError
In case any gradient cannot be computed (e.g. if gradient function not implemented).
Expand source code
def get_gradients(self, loss, params):
  """Returns gradients of `loss` with respect to `params`.

  Should be used only in legacy v1 graph mode.

  Args:
    loss: Loss tensor.
    params: List of variables.

  Returns:
    List of gradient tensors.

  Raises:
    ValueError: In case any gradient cannot be computed (e.g. if gradient
      function not implemented).
  """
  params = tf.nest.flatten(params)
  with backend.get_graph().as_default(), backend.name_scope(self._name +
                                                            "/gradients"):
    grads = tf.compat.v1.gradients(loss, params)
    for grad, param in zip(grads, params):
      if grad is None:
        raise ValueError("Variable {} has `None` for gradient. "
                         "Please make sure that all of your ops have a "
                         "gradient defined (i.e. are differentiable). "
                         "Common ops without gradient: "
                         "K.argmax, K.round, K.eval.".format(param))
  return grads
def get_slot(self, var, slot_name)
Expand source code
def get_slot(self, var, slot_name):
  var_key = _var_key(var)
  slot_dict = self._slots[var_key]
  return slot_dict[slot_name]
def get_slot_names(self)

A list of names for this optimizer's slots.

Expand source code
def get_slot_names(self):
  """A list of names for this optimizer's slots."""
  return self._slot_names
def get_updates(self, loss, params)
Expand source code
def get_updates(self, loss, params):
  grads = self.get_gradients(loss, params)
  grads_and_vars = list(zip(grads, params))
  self._assert_valid_dtypes([
      v for g, v in grads_and_vars
      if g is not None and v.dtype != tf.resource
  ])
  return [self.apply_gradients(grads_and_vars)]
def get_weights(self)

Returns the current weights of the optimizer.

The weights of an optimizer are its state (ie, variables). This function returns the weight values associated with this optimizer as a list of Numpy arrays. The first value is always the iterations count of the optimizer, followed by the optimizer's state variables in the order they were created. The returned list can in turn be used to load state into similarly parameterized optimizers.

For example, the RMSprop optimizer for this simple model returns a list of three values– the iteration count, followed by the root-mean-square value of the kernel and bias of the single Dense layer:

>>> opt = tf.keras.optimizers.RMSprop()
>>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
>>> m.compile(opt, loss='mse')
>>> data = np.arange(100).reshape(5, 20)
>>> labels = np.zeros(5)
>>> print('Training'); results = m.fit(data, labels)
Training ...
>>> len(opt.get_weights())
3

Returns

Weights values as a list of numpy arrays.

Expand source code
def get_weights(self):
  """Returns the current weights of the optimizer.

  The weights of an optimizer are its state (ie, variables).
  This function returns the weight values associated with this
  optimizer as a list of Numpy arrays. The first value is always the
  iterations count of the optimizer, followed by the optimizer's state
  variables in the order they were created. The returned list can in turn
  be used to load state into similarly parameterized optimizers.

  For example, the RMSprop optimizer for this simple model returns a list of
  three values-- the iteration count, followed by the root-mean-square value
  of the kernel and bias of the single Dense layer:

  >>> opt = tf.keras.optimizers.RMSprop()
  >>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
  >>> m.compile(opt, loss='mse')
  >>> data = np.arange(100).reshape(5, 20)
  >>> labels = np.zeros(5)
  >>> print('Training'); results = m.fit(data, labels)
  Training ...
  >>> len(opt.get_weights())
  3

  Returns:
      Weights values as a list of numpy arrays.
  """
  params = self.weights
  return backend.batch_get_value(params)
def minimize(self, loss, var_list, grad_loss=None, name=None, tape=None)

Minimize loss by updating var_list.

This method simply computes gradient using tf.GradientTape and calls apply_gradients(). If you want to process the gradient before applying then call tf.GradientTape and apply_gradients() explicitly instead of using this function.

Args

loss
Tensor or callable. If a callable, loss should take no arguments and return the value to minimize. If a Tensor, the tape argument must be passed.
var_list
list or tuple of Variable objects to update to minimize loss, or a callable returning the list or tuple of Variable objects. Use callable when the variable list would otherwise be incomplete before minimize since the variables are created at the first time loss is called.
grad_loss
(Optional). A Tensor holding the gradient computed for loss.
name
(Optional) str. Name for the returned operation.
tape
(Optional) tf.GradientTape. If loss is provided as a Tensor, the tape that computed the loss must be provided.

Returns

An Operation that updates the variables in var_list. The iterations will be automatically increased by 1.

Raises

ValueError
If some of the variables are not Variable objects.
Expand source code
def minimize(self, loss, var_list, grad_loss=None, name=None, tape=None):
  """Minimize `loss` by updating `var_list`.

  This method simply computes gradient using `tf.GradientTape` and calls
  `apply_gradients()`. If you want to process the gradient before applying
  then call `tf.GradientTape` and `apply_gradients()` explicitly instead
  of using this function.

  Args:
    loss: `Tensor` or callable. If a callable, `loss` should take no arguments
      and return the value to minimize. If a `Tensor`, the `tape` argument
      must be passed.
    var_list: list or tuple of `Variable` objects to update to minimize
      `loss`, or a callable returning the list or tuple of `Variable` objects.
      Use callable when the variable list would otherwise be incomplete before
      `minimize` since the variables are created at the first time `loss` is
      called.
    grad_loss: (Optional). A `Tensor` holding the gradient computed for
      `loss`.
    name: (Optional) str. Name for the returned operation.
    tape: (Optional) `tf.GradientTape`. If `loss` is provided as a `Tensor`,
      the tape that computed the `loss` must be provided.

  Returns:
    An `Operation` that updates the variables in `var_list`. The `iterations`
    will be automatically increased by 1.

  Raises:
    ValueError: If some of the variables are not `Variable` objects.

  """
  grads_and_vars = self._compute_gradients(
      loss, var_list=var_list, grad_loss=grad_loss, tape=tape)
  return self.apply_gradients(grads_and_vars, name=name)
def set_weights(self, weights)

Set the weights of the optimizer.

The weights of an optimizer are its state (ie, variables). This function takes the weight values associated with this optimizer as a list of Numpy arrays. The first value is always the iterations count of the optimizer, followed by the optimizer's state variables in the order they are created. The passed values are used to set the new state of the optimizer.

For example, the RMSprop optimizer for this simple model takes a list of three values– the iteration count, followed by the root-mean-square value of the kernel and bias of the single Dense layer:

>>> opt = tf.keras.optimizers.RMSprop()
>>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
>>> m.compile(opt, loss='mse')
>>> data = np.arange(100).reshape(5, 20)
>>> labels = np.zeros(5)
>>> print('Training'); results = m.fit(data, labels)
Training ...
>>> new_weights = [np.array(10), np.ones([20, 10]), np.zeros([10])]
>>> opt.set_weights(new_weights)
>>> opt.iterations
<tf.Variable 'RMSprop/iter:0' shape=() dtype=int64, numpy=10>

Args

weights
weight values as a list of numpy arrays.
Expand source code
def set_weights(self, weights):
  """Set the weights of the optimizer.

  The weights of an optimizer are its state (ie, variables).
  This function takes the weight values associated with this
  optimizer as a list of Numpy arrays. The first value is always the
  iterations count of the optimizer, followed by the optimizer's state
  variables in the order they are created. The passed values are used to set
  the new state of the optimizer.

  For example, the RMSprop optimizer for this simple model takes a list of
  three values-- the iteration count, followed by the root-mean-square value
  of the kernel and bias of the single Dense layer:

  >>> opt = tf.keras.optimizers.RMSprop()
  >>> m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
  >>> m.compile(opt, loss='mse')
  >>> data = np.arange(100).reshape(5, 20)
  >>> labels = np.zeros(5)
  >>> print('Training'); results = m.fit(data, labels)
  Training ...
  >>> new_weights = [np.array(10), np.ones([20, 10]), np.zeros([10])]
  >>> opt.set_weights(new_weights)
  >>> opt.iterations
  <tf.Variable 'RMSprop/iter:0' shape=() dtype=int64, numpy=10>

  Args:
      weights: weight values as a list of numpy arrays.
  """
  params = self.weights
  if len(params) != len(weights):
    raise ValueError(
        "You called `set_weights(weights)` on optimizer " + self._name +
        " with a  weight list of length " + str(len(weights)) +
        ", but the optimizer was expecting " + str(len(params)) +
        " weights. Provided weights: " + str(weights)[:50] + "...")
  if not params:
    return
  weight_value_tuples = []
  param_values = backend.batch_get_value(params)
  for pv, p, w in zip(param_values, params, weights):
    if pv.shape != w.shape:
      raise ValueError("Optimizer weight shape " + str(pv.shape) +
                       " not compatible with "
                       "provided weight shape " + str(w.shape))
    weight_value_tuples.append((p, w))
  backend.batch_set_value(weight_value_tuples)
def variables(self)

Returns variables of this Optimizer based on the order created.

Expand source code
def variables(self):
  """Returns variables of this Optimizer based on the order created."""
  return self._weights
class RMSprop (learning_rate=0.001, rho=0.9, momentum=0.0, epsilon=1e-07, centered=False, name='RMSprop', **kwargs)

Optimizer that implements the RMSprop algorithm.

The gist of RMSprop is to:

  • Maintain a moving (discounted) average of the square of gradients
  • Divide the gradient by the root of this average

This implementation of RMSprop uses plain momentum, not Nesterov momentum.

The centered version additionally maintains a moving average of the gradients, and uses that average to estimate the variance.

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.001.
rho
Discounting factor for the history/coming gradient. Defaults to 0.9.
momentum
A scalar or a scalar Tensor. Defaults to 0.0.
epsilon
A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to 1e-7.
centered
Boolean. If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False.
name
Optional name prefix for the operations created when applying gradients. Defaults to "RMSprop".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Note that in the dense implementation of this algorithm, variables and their corresponding accumulators (momentum, gradient moving average, square gradient moving average) will be updated even if the gradient is zero (i.e. accumulators will decay, momentum will be applied). The sparse implementation (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) will not update variable slices or their accumulators unless those slices were used in the forward pass (nor is there an "eventual" correction to account for these omitted updates). This leads to more efficient updates for large embedding lookup tables (where most of the slices are not accessed in a particular graph execution), but differs from the published algorithm.

Usage:

>>> opt = tf.keras.optimizers.RMSprop(learning_rate=0.1)
>>> var1 = tf.Variable(10.0)
>>> loss = lambda: (var1 ** 2) / 2.0    # d(loss) / d(var1) = var1
>>> step_count = opt.minimize(loss, [var1]).numpy()
>>> var1.numpy()
9.683772

Reference

Construct a new RMSprop optimizer.

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.001.
rho
Discounting factor for the history/coming gradient. Defaults to 0.9.
momentum
A scalar or a scalar Tensor. Defaults to 0.0.
epsilon
A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to 1e-7.
centered
Boolean. If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False.
name
Optional name prefix for the operations created when applying gradients. Defaults to "RMSprop".
**kwargs
keyword arguments. Allowed to be {clipnorm, clipvalue, lr, decay}. clipnorm is clip gradients by norm; clipvalue is clip gradients by value, decay is included for backward compatibility to allow time inverse decay of learning rate. lr is included for backward compatibility, recommended to use learning_rate instead.

@compatibility(eager) When eager execution is enabled, learning_rate, decay, momentum, and epsilon can each be a callable that takes no arguments and returns the actual value to use. This can be useful for changing these values across different invocations of optimizer functions. @end_compatibility

Expand source code
class RMSprop(optimizer_v2.OptimizerV2):
  r"""Optimizer that implements the RMSprop algorithm.

  The gist of RMSprop is to:

  - Maintain a moving (discounted) average of the square of gradients
  - Divide the gradient by the root of this average

  This implementation of RMSprop uses plain momentum, not Nesterov momentum.

  The centered version additionally maintains a moving average of the
  gradients, and uses that average to estimate the variance.

  Args:
    learning_rate: A `Tensor`, floating point value, or a schedule that is a
      `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
      that takes no arguments and returns the actual value to use. The
      learning rate. Defaults to 0.001.
    rho: Discounting factor for the history/coming gradient. Defaults to 0.9.
    momentum: A scalar or a scalar `Tensor`. Defaults to 0.0.
    epsilon: A small constant for numerical stability. This epsilon is
      "epsilon hat" in the Kingma and Ba paper (in the formula just before
      Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
      1e-7.
    centered: Boolean. If `True`, gradients are normalized by the estimated
      variance of the gradient; if False, by the uncentered second moment.
      Setting this to `True` may help with training, but is slightly more
      expensive in terms of computation and memory. Defaults to `False`.
    name: Optional name prefix for the operations created when applying
      gradients. Defaults to `"RMSprop"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Note that in the dense implementation of this algorithm, variables and their
  corresponding accumulators (momentum, gradient moving average, square
  gradient moving average) will be updated even if the gradient is zero
  (i.e. accumulators will decay, momentum will be applied). The sparse
  implementation (used when the gradient is an `IndexedSlices` object,
  typically because of `tf.gather` or an embedding lookup in the forward pass)
  will not update variable slices or their accumulators unless those slices
  were used in the forward pass (nor is there an "eventual" correction to
  account for these omitted updates). This leads to more efficient updates for
  large embedding lookup tables (where most of the slices are not accessed in
  a particular graph execution), but differs from the published algorithm.

  Usage:

  >>> opt = tf.keras.optimizers.RMSprop(learning_rate=0.1)
  >>> var1 = tf.Variable(10.0)
  >>> loss = lambda: (var1 ** 2) / 2.0    # d(loss) / d(var1) = var1
  >>> step_count = opt.minimize(loss, [var1]).numpy()
  >>> var1.numpy()
  9.683772

  Reference:
    - [Hinton, 2012](
      http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.001,
               rho=0.9,
               momentum=0.0,
               epsilon=1e-7,
               centered=False,
               name="RMSprop",
               **kwargs):
    """Construct a new RMSprop optimizer.

    Args:
      learning_rate: A `Tensor`, floating point value, or a schedule that is a
        `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
        that takes no arguments and returns the actual value to use. The
        learning rate. Defaults to 0.001.
      rho: Discounting factor for the history/coming gradient. Defaults to 0.9.
      momentum: A scalar or a scalar `Tensor`. Defaults to 0.0.
      epsilon: A small constant for numerical stability. This epsilon is
        "epsilon hat" in the Kingma and Ba paper (in the formula just before
        Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
        1e-7.
      centered: Boolean. If `True`, gradients are normalized by the estimated
        variance of the gradient; if False, by the uncentered second moment.
        Setting this to `True` may help with training, but is slightly more
        expensive in terms of computation and memory. Defaults to `False`.
      name: Optional name prefix for the operations created when applying
        gradients. Defaults to "RMSprop".
      **kwargs: keyword arguments. Allowed to be {`clipnorm`, `clipvalue`, `lr`,
        `decay`}. `clipnorm` is clip gradients by norm; `clipvalue` is clip
        gradients by value, `decay` is included for backward compatibility to
        allow time inverse decay of learning rate. `lr` is included for backward
        compatibility, recommended to use `learning_rate` instead.

    @compatibility(eager)
    When eager execution is enabled, `learning_rate`, `decay`, `momentum`, and
    `epsilon` can each be a callable that takes no arguments and returns the
    actual value to use. This can be useful for changing these values across
    different invocations of optimizer functions.
    @end_compatibility
    """
    super(RMSprop, self).__init__(name, **kwargs)
    self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
    self._set_hyper("decay", self._initial_decay)
    self._set_hyper("rho", rho)

    self._momentum = False
    if isinstance(momentum, tf.Tensor) or callable(momentum) or momentum > 0:
      self._momentum = True
    if isinstance(momentum, (int, float)) and (momentum < 0 or momentum > 1):
      raise ValueError("`momentum` must be between [0, 1].")
    self._set_hyper("momentum", momentum)

    self.epsilon = epsilon or backend_config.epsilon()
    self.centered = centered

  def _create_slots(self, var_list):
    for var in var_list:
      self.add_slot(var, "rms")
    if self._momentum:
      for var in var_list:
        self.add_slot(var, "momentum")
    if self.centered:
      for var in var_list:
        self.add_slot(var, "mg")

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(RMSprop, self)._prepare_local(var_device, var_dtype, apply_state)

    rho = tf.identity(self._get_hyper("rho", var_dtype))
    apply_state[(var_device, var_dtype)].update(
        dict(
            neg_lr_t=-apply_state[(var_device, var_dtype)]["lr_t"],
            epsilon=tf.convert_to_tensor(
                self.epsilon, var_dtype),
            rho=rho,
            momentum=tf.identity(self._get_hyper("momentum", var_dtype)),
            one_minus_rho=1. - rho))

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    rms = self.get_slot(var, "rms")
    if self._momentum:
      mom = self.get_slot(var, "momentum")
      if self.centered:
        mg = self.get_slot(var, "mg")
        return tf.raw_ops.ResourceApplyCenteredRMSProp(
            var=var.handle,
            mg=mg.handle,
            ms=rms.handle,
            mom=mom.handle,
            lr=coefficients["lr_t"],
            rho=coefficients["rho"],
            momentum=coefficients["momentum"],
            epsilon=coefficients["epsilon"],
            grad=grad,
            use_locking=self._use_locking)
      else:
        return tf.raw_ops.ResourceApplyRMSProp(
            var=var.handle,
            ms=rms.handle,
            mom=mom.handle,
            lr=coefficients["lr_t"],
            rho=coefficients["rho"],
            momentum=coefficients["momentum"],
            epsilon=coefficients["epsilon"],
            grad=grad,
            use_locking=self._use_locking)
    else:
      rms_t = (coefficients["rho"] * rms +
               coefficients["one_minus_rho"] * tf.square(grad))
      rms_t = tf.compat.v1.assign(rms, rms_t, use_locking=self._use_locking)
      denom_t = rms_t
      if self.centered:
        mg = self.get_slot(var, "mg")
        mg_t = coefficients["rho"] * mg + coefficients["one_minus_rho"] * grad
        mg_t = tf.compat.v1.assign(mg, mg_t, use_locking=self._use_locking)
        denom_t = rms_t - tf.square(mg_t)
      var_t = var - coefficients["lr_t"] * grad / (
          tf.sqrt(denom_t) + coefficients["epsilon"])
      return tf.compat.v1.assign(var, var_t, use_locking=self._use_locking).op

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    rms = self.get_slot(var, "rms")
    if self._momentum:
      mom = self.get_slot(var, "momentum")
      if self.centered:
        mg = self.get_slot(var, "mg")
        return tf.raw_ops.ResourceSparseApplyCenteredRMSProp(
            var=var.handle,
            mg=mg.handle,
            ms=rms.handle,
            mom=mom.handle,
            lr=coefficients["lr_t"],
            rho=coefficients["rho"],
            momentum=coefficients["momentum"],
            epsilon=coefficients["epsilon"],
            grad=grad,
            indices=indices,
            use_locking=self._use_locking)
      else:
        return tf.raw_ops.ResourceSparseApplyRMSProp(
            var=var.handle,
            ms=rms.handle,
            mom=mom.handle,
            lr=coefficients["lr_t"],
            rho=coefficients["rho"],
            momentum=coefficients["momentum"],
            epsilon=coefficients["epsilon"],
            grad=grad,
            indices=indices,
            use_locking=self._use_locking)
    else:
      rms_scaled_g_values = (grad * grad) * coefficients["one_minus_rho"]
      rms_t = tf.compat.v1.assign(rms, rms * coefficients["rho"],
                               use_locking=self._use_locking)
      with tf.control_dependencies([rms_t]):
        rms_t = self._resource_scatter_add(rms, indices, rms_scaled_g_values)
        rms_slice = tf.gather(rms_t, indices)
      denom_slice = rms_slice
      if self.centered:
        mg = self.get_slot(var, "mg")
        mg_scaled_g_values = grad * coefficients["one_minus_rho"]
        mg_t = tf.compat.v1.assign(mg, mg * coefficients["rho"],
                                use_locking=self._use_locking)
        with tf.control_dependencies([mg_t]):
          mg_t = self._resource_scatter_add(mg, indices, mg_scaled_g_values)
          mg_slice = tf.gather(mg_t, indices)
          denom_slice = rms_slice - tf.square(mg_slice)
      var_update = self._resource_scatter_add(
          var, indices, coefficients["neg_lr_t"] * grad / (
              tf.sqrt(denom_slice) + coefficients["epsilon"]))
      if self.centered:
        return tf.group(*[var_update, rms_t, mg_t])
      return tf.group(*[var_update, rms_t])

  def set_weights(self, weights):
    params = self.weights
    # Override set_weights for backward compatibility of Keras V1 optimizer
    # since it does not include iteration at head of the weight list. Set
    # iteration to 0.
    if len(params) == len(weights) + 1:
      weights = [np.array(0)] + weights
    super(RMSprop, self).set_weights(weights)

  def get_config(self):
    config = super(RMSprop, self).get_config()
    config.update({
        "learning_rate": self._serialize_hyperparameter("learning_rate"),
        "decay": self._initial_decay,
        "rho": self._serialize_hyperparameter("rho"),
        "momentum": self._serialize_hyperparameter("momentum"),
        "epsilon": self.epsilon,
        "centered": self.centered,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members

class SGD (learning_rate=0.01, momentum=0.0, nesterov=False, name='SGD', **kwargs)

Gradient descent (with momentum) optimizer.

Update rule for parameter w with gradient g when momentum is 0:

w = w - learning_rate * g

Update rule when momentum is larger than 0:

velocity = momentum * velocity - learning_rate * g
w = w + velocity

When nesterov=True, this rule becomes:

velocity = momentum * velocity - learning_rate * g
w = w + momentum * velocity - learning_rate * g

Args

learning_rate
A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.01.
momentum
float hyperparameter >= 0 that accelerates gradient descent in the relevant direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient descent.
nesterov
boolean. Whether to apply Nesterov momentum. Defaults to False.
name
Optional name prefix for the operations created when applying gradients. Defaults to "SGD".
**kwargs
Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.

Usage:

>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1)
>>> var = tf.Variable(1.0)
>>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> # Step is `- learning_rate * grad`
>>> var.numpy()
0.9
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9)
>>> var = tf.Variable(1.0)
>>> val0 = var.value()
>>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
>>> # First step is `- learning_rate * grad`
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val1 = var.value()
>>> (val0 - val1).numpy()
0.1
>>> # On later steps, step-size increases because of momentum
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val2 = var.value()
>>> (val1 - val2).numpy()
0.18

Reference

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class is stateful and thread-compatible.

Example of custom gradient transformations:

def my_gradient_transformer(grads_and_vars):
  # Simple example, double the gradients.
  return [(2. * g, v) for g, v in grads_and_vars]

optimizer = tf.keras.optimizers.SGD(
    1e-3, gradient_transformers=[my_gradient_transformer])

Args

name
String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
The function to use to aggregate gradients across devices (when using tf.distribute.Strategy). If None, defaults to summing the gradients across devices. The function should accept and return a list of (gradient, variable) tuples.
gradient_transformers
Optional. List of functions to use to transform gradients before applying updates to Variables. The functions are applied after gradient_aggregator. The functions should accept and return a list of (gradient, variable) tuples.
**kwargs
keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Raises

ValueError
in case of any invalid argument.
Expand source code
class SGD(optimizer_v2.OptimizerV2):
  r"""Gradient descent (with momentum) optimizer.

  Update rule for parameter `w` with gradient `g` when `momentum` is 0:

  ```python
  w = w - learning_rate * g
  ```

  Update rule when `momentum` is larger than 0:

  ```python
  velocity = momentum * velocity - learning_rate * g
  w = w + velocity
  ```

  When `nesterov=True`, this rule becomes:

  ```python
  velocity = momentum * velocity - learning_rate * g
  w = w + momentum * velocity - learning_rate * g
  ```

  Args:
    learning_rate: A `Tensor`, floating point value, or a schedule that is a
      `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
      that takes no arguments and returns the actual value to use. The
      learning rate. Defaults to 0.01.
    momentum: float hyperparameter >= 0 that accelerates gradient descent
      in the relevant
      direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient
      descent.
    nesterov: boolean. Whether to apply Nesterov momentum.
      Defaults to `False`.
    name: Optional name prefix for the operations created when applying
      gradients.  Defaults to `"SGD"`.
    **kwargs: Keyword arguments. Allowed to be one of
      `"clipnorm"` or `"clipvalue"`.
      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
      gradients by value.

  Usage:

  >>> opt = tf.keras.optimizers.SGD(learning_rate=0.1)
  >>> var = tf.Variable(1.0)
  >>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
  >>> step_count = opt.minimize(loss, [var]).numpy()
  >>> # Step is `- learning_rate * grad`
  >>> var.numpy()
  0.9

  >>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9)
  >>> var = tf.Variable(1.0)
  >>> val0 = var.value()
  >>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
  >>> # First step is `- learning_rate * grad`
  >>> step_count = opt.minimize(loss, [var]).numpy()
  >>> val1 = var.value()
  >>> (val0 - val1).numpy()
  0.1
  >>> # On later steps, step-size increases because of momentum
  >>> step_count = opt.minimize(loss, [var]).numpy()
  >>> val2 = var.value()
  >>> (val1 - val2).numpy()
  0.18

  Reference:
      - For `nesterov=True`, See [Sutskever et al., 2013](
        http://jmlr.org/proceedings/papers/v28/sutskever13.pdf).
  """

  _HAS_AGGREGATE_GRAD = True

  def __init__(self,
               learning_rate=0.01,
               momentum=0.0,
               nesterov=False,
               name="SGD",
               **kwargs):
    super(SGD, self).__init__(name, **kwargs)
    self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
    self._set_hyper("decay", self._initial_decay)

    self._momentum = False
    if isinstance(momentum, tf.Tensor) or callable(momentum) or momentum > 0:
      self._momentum = True
    if isinstance(momentum, (int, float)) and (momentum < 0 or momentum > 1):
      raise ValueError("`momentum` must be between [0, 1].")
    self._set_hyper("momentum", momentum)

    self.nesterov = nesterov

  def _create_slots(self, var_list):
    if self._momentum:
      for var in var_list:
        self.add_slot(var, "momentum")

  def _prepare_local(self, var_device, var_dtype, apply_state):
    super(SGD, self)._prepare_local(var_device, var_dtype, apply_state)
    apply_state[(var_device, var_dtype)]["momentum"] = tf.identity(
        self._get_hyper("momentum", var_dtype))

  def _resource_apply_dense(self, grad, var, apply_state=None):
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    if self._momentum:
      momentum_var = self.get_slot(var, "momentum")
      return tf.raw_ops.ResourceApplyKerasMomentum(
          var=var.handle,
          accum=momentum_var.handle,
          lr=coefficients["lr_t"],
          grad=grad,
          momentum=coefficients["momentum"],
          use_locking=self._use_locking,
          use_nesterov=self.nesterov)
    else:
      return tf.raw_ops.ResourceApplyGradientDescent(
          var=var.handle,
          alpha=coefficients["lr_t"],
          delta=grad,
          use_locking=self._use_locking)

  def _resource_apply_sparse_duplicate_indices(self, grad, var, indices,
                                               **kwargs):
    if self._momentum:
      return super(SGD, self)._resource_apply_sparse_duplicate_indices(
          grad, var, indices, **kwargs)
    else:
      var_device, var_dtype = var.device, var.dtype.base_dtype
      coefficients = (kwargs.get("apply_state", {}).get((var_device, var_dtype))
                      or self._fallback_apply_state(var_device, var_dtype))

      return tf.raw_ops.ResourceScatterAdd(
          resource=var.handle,
          indices=indices,
          updates=-grad * coefficients["lr_t"])

  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
    # This method is only needed for momentum optimization.
    var_device, var_dtype = var.device, var.dtype.base_dtype
    coefficients = ((apply_state or {}).get((var_device, var_dtype))
                    or self._fallback_apply_state(var_device, var_dtype))

    momentum_var = self.get_slot(var, "momentum")
    return tf.raw_ops.ResourceSparseApplyKerasMomentum(
        var=var.handle,
        accum=momentum_var.handle,
        lr=coefficients["lr_t"],
        grad=grad,
        indices=indices,
        momentum=coefficients["momentum"],
        use_locking=self._use_locking,
        use_nesterov=self.nesterov)

  def get_config(self):
    config = super(SGD, self).get_config()
    config.update({
        "learning_rate": self._serialize_hyperparameter("learning_rate"),
        "decay": self._initial_decay,
        "momentum": self._serialize_hyperparameter("momentum"),
        "nesterov": self.nesterov,
    })
    return config

Ancestors

  • OptimizerV2
  • tensorflow.python.training.tracking.base.Trackable

Inherited members