Module keras.optimizer_v2.nadam
Nadam optimizer implementation.
Expand source code
# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
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# See the License for the specific language governing permissions and
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# ==============================================================================
"""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
). IfNone
, 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
. Ifclipvalue
(float) is set, the gradient of each weight is clipped to be no higher than this value. Ifclipnorm
(float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. Ifglobal_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