1# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
2#
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7#     http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14# ==============================================================================
15"""Nadam optimizer implementation."""
16# pylint: disable=g-classes-have-attributes
17from __future__ import absolute_import
18from __future__ import division
19from __future__ import print_function
20
21from tensorflow.python.framework import ops
22from tensorflow.python.keras import backend_config
23from tensorflow.python.keras.optimizer_v2 import learning_rate_schedule
24from tensorflow.python.keras.optimizer_v2 import optimizer_v2
25from tensorflow.python.ops import array_ops
26from tensorflow.python.ops import control_flow_ops
27from tensorflow.python.ops import math_ops
28from tensorflow.python.ops import state_ops
29from tensorflow.python.ops import variables as tf_variables
30from tensorflow.python.util.tf_export import keras_export
31
32
33@keras_export('keras.optimizers.Nadam')
34class Nadam(optimizer_v2.OptimizerV2):
35  r"""Optimizer that implements the NAdam algorithm.
36  Much like Adam is essentially RMSprop with momentum, Nadam is Adam with
37  Nesterov momentum.
38
39  Args:
40    learning_rate: A Tensor or a floating point value.  The learning rate.
41    beta_1: A float value or a constant float tensor. The exponential decay
42      rate for the 1st moment estimates.
43    beta_2: A float value or a constant float tensor. The exponential decay
44      rate for the exponentially weighted infinity norm.
45    epsilon: A small constant for numerical stability.
46    name: Optional name for the operations created when applying gradients.
47      Defaults to `"Nadam"`.
48    **kwargs: Keyword arguments. Allowed to be one of
49      `"clipnorm"` or `"clipvalue"`.
50      `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
51      gradients by value.
52
53  Usage Example:
54    >>> opt = tf.keras.optimizers.Nadam(learning_rate=0.2)
55    >>> var1 = tf.Variable(10.0)
56    >>> loss = lambda: (var1 ** 2) / 2.0
57    >>> step_count = opt.minimize(loss, [var1]).numpy()
58    >>> "{:.1f}".format(var1.numpy())
59    9.8
60
61  Reference:
62    - [Dozat, 2015](http://cs229.stanford.edu/proj2015/054_report.pdf).
63  """
64
65  _HAS_AGGREGATE_GRAD = True
66
67  def __init__(self,
68               learning_rate=0.001,
69               beta_1=0.9,
70               beta_2=0.999,
71               epsilon=1e-7,
72               name='Nadam',
73               **kwargs):
74    # Backwards compatibility with keras NAdam optimizer.
75    kwargs['decay'] = kwargs.pop('schedule_decay', 0.004)
76    learning_rate = kwargs.get('lr', learning_rate)
77    if isinstance(learning_rate, learning_rate_schedule.LearningRateSchedule):
78      raise ValueError('The Nadam optimizer does not support '
79                       'tf.keras.optimizers.LearningRateSchedules as the '
80                       'learning rate.')
81
82    super(Nadam, self).__init__(name, **kwargs)
83    self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
84    self._set_hyper('decay', self._initial_decay)
85    self._set_hyper('beta_1', beta_1)
86    self._set_hyper('beta_2', beta_2)
87    self.epsilon = epsilon or backend_config.epsilon()
88    self._m_cache = None
89
90  def _create_slots(self, var_list):
91    var_dtype = var_list[0].dtype.base_dtype
92    if self._m_cache is None:
93      self._m_cache = self.add_weight(
94          'momentum_cache',
95          shape=[],
96          dtype=var_dtype,
97          initializer='ones',
98          trainable=False,
99          aggregation=tf_variables.VariableAggregation.ONLY_FIRST_REPLICA)
100      self._weights.append(self._m_cache)
101    # Separate for-loops to respect the ordering of slot variables from v1.
102    for var in var_list:
103      # Create slots for the first moments.
104      self.add_slot(var, 'm')
105    for var in var_list:
106      # Create slots for the second moments.
107      self.add_slot(var, 'v')
108
109  def _prepare_local(self, var_device, var_dtype, apply_state):
110    lr_t = array_ops.identity(self._get_hyper('learning_rate', var_dtype))
111    beta_1_t = array_ops.identity(self._get_hyper('beta_1', var_dtype))
112    beta_2_t = array_ops.identity(self._get_hyper('beta_2', var_dtype))
113    local_step = math_ops.cast(self.iterations + 1, var_dtype)
114    next_step = math_ops.cast(self.iterations + 2, var_dtype)
115
116    decay_base = math_ops.cast(0.96, var_dtype)
117
118    m_t = beta_1_t * (1. - 0.5 * (
119        math_ops.pow(decay_base, self._initial_decay * local_step)))
120    m_t_1 = beta_1_t * (1. - 0.5 * (
121        math_ops.pow(decay_base, self._initial_decay * next_step)))
122
123    m_schedule_new = math_ops.cast(self._m_cache_read, var_dtype) * m_t
124    if var_dtype is self._m_cache.dtype:
125      m_schedule_new = array_ops.identity(state_ops.assign(
126          self._m_cache, m_schedule_new, use_locking=self._use_locking))
127    m_schedule_next = m_schedule_new * m_t_1
128
129    apply_state[(var_device, var_dtype)] = dict(
130        lr_t=lr_t,
131        neg_lr_t=-lr_t,
132        epsilon=ops.convert_to_tensor_v2_with_dispatch(self.epsilon, var_dtype),
133        beta_1_t=beta_1_t,
134        beta_2_t=beta_2_t,
135        m_t=m_t,
136        m_t_1=m_t_1,
137        one_minus_beta_1_t=1 - beta_1_t,
138        one_minus_beta_2_t=1 - beta_2_t,
139        one_minus_m_t=1. - m_t,
140        one_minus_m_schedule_new=1. - m_schedule_new,
141        one_minus_m_schedule_next=1. - m_schedule_next,
142        v_t_prime_denominator=1. - math_ops.pow(beta_2_t, local_step),
143    )
144
145  def _prepare(self, var_list):
146    # Get the value of the momentum cache before starting to apply gradients.
147    self._m_cache_read = array_ops.identity(self._m_cache)
148    return super(Nadam, self)._prepare(var_list)
149
150  def _resource_apply_dense(self, grad, var, apply_state=None):
151    var_device, var_dtype = var.device, var.dtype.base_dtype
152    coefficients = ((apply_state or {}).get((var_device, var_dtype))
153                    or self._fallback_apply_state(var_device, var_dtype))
154
155    m = self.get_slot(var, 'm')
156    v = self.get_slot(var, 'v')
157
158    g_prime = grad / coefficients['one_minus_m_schedule_new']
159    m_t = (coefficients['beta_1_t'] * m +
160           coefficients['one_minus_beta_1_t'] * grad)
161    m_t = state_ops.assign(m, m_t, use_locking=self._use_locking)
162    m_t_prime = m_t / coefficients['one_minus_m_schedule_next']
163    v_t = (coefficients['beta_2_t'] * v +
164           coefficients['one_minus_beta_2_t'] * math_ops.square(grad))
165    v_t = state_ops.assign(v, v_t, use_locking=self._use_locking)
166    v_t_prime = v_t / coefficients['v_t_prime_denominator']
167    m_t_bar = (coefficients['one_minus_m_t'] * g_prime +
168               coefficients['m_t_1'] * m_t_prime)
169    var_t = var - coefficients['lr_t'] * m_t_bar / (
170        math_ops.sqrt(v_t_prime) + coefficients['epsilon'])
171    return state_ops.assign(var, var_t, use_locking=self._use_locking).op
172
173  def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
174    var_device, var_dtype = var.device, var.dtype.base_dtype
175    coefficients = ((apply_state or {}).get((var_device, var_dtype))
176                    or self._fallback_apply_state(var_device, var_dtype))
177
178    m = self.get_slot(var, 'm')
179    v = self.get_slot(var, 'v')
180
181    g_prime = grad / coefficients['one_minus_m_schedule_new']
182
183    # m_t = beta1 * m + (1 - beta1) * g_t
184    m_scaled_g_values = grad * coefficients['one_minus_beta_1_t']
185    m_t = state_ops.assign(m, m * coefficients['beta_1_t'],
186                           use_locking=self._use_locking)
187
188    with ops.control_dependencies([m_t]):
189      m_t = self._resource_scatter_add(m, indices, m_scaled_g_values)
190      m_t_slice = array_ops.gather(m_t, indices)
191
192    m_t_prime = m_t_slice / coefficients['one_minus_m_schedule_next']
193    m_t_bar = (coefficients['one_minus_m_t'] * g_prime +
194               coefficients['m_t_1'] * m_t_prime)
195
196    # v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
197    v_scaled_g_values = (grad * grad) * coefficients['one_minus_beta_2_t']
198    v_t = state_ops.assign(v, v * coefficients['beta_2_t'],
199                           use_locking=self._use_locking)
200
201    with ops.control_dependencies([v_t]):
202      v_t = self._resource_scatter_add(v, indices, v_scaled_g_values)
203      v_t_slice = array_ops.gather(v_t, indices)
204
205    v_t_prime = v_t_slice / coefficients['v_t_prime_denominator']
206    v_prime_sqrt_plus_eps = math_ops.sqrt(v_t_prime) + coefficients['epsilon']
207
208    var_update = self._resource_scatter_add(
209        var, indices,
210        coefficients['neg_lr_t'] * m_t_bar / v_prime_sqrt_plus_eps)
211    return control_flow_ops.group(*[var_update, m_t_bar, v_t])
212
213  def get_config(self):
214    config = super(Nadam, self).get_config()
215    config.update({
216        'learning_rate': self._serialize_hyperparameter('learning_rate'),
217        'decay': self._initial_decay,
218        'beta_1': self._serialize_hyperparameter('beta_1'),
219        'beta_2': self._serialize_hyperparameter('beta_2'),
220        'epsilon': self.epsilon,
221    })
222    return config
223