Module keras.optimizer_v2.nadam

Nadam optimizer implementation.

Expand source code
# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Nadam optimizer implementation."""

import tensorflow.compat.v2 as tf
from keras import backend_config
from keras.optimizer_v2 import learning_rate_schedule
from keras.optimizer_v2 import optimizer_v2
from tensorflow.python.util.tf_export import keras_export


@keras_export('keras.optimizers.Nadam')
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

Classes

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