# Copyright 2021 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. # ============================================================================== """Adam optimizer implementation.""" import tensorflow.compat.v2 as tf from keras.optimizers.optimizer_experimental import optimizer from keras.utils import generic_utils # isort: off from tensorflow.python.util.tf_export import keras_export @generic_utils.register_keras_serializable() @keras_export("keras.optimizers.experimental.Adam", v1=[]) class Adam(optimizer.Optimizer): 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 `tf.Tensor`, floating point value, 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`. {{base_optimizer_keyword_args}} 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). """ def __init__( self, learning_rate=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-7, amsgrad=False, clipnorm=None, clipvalue=None, global_clipnorm=None, use_ema=False, ema_momentum=0.99, ema_overwrite_frequency=None, jit_compile=True, name="Adam", **kwargs ): super().__init__( name=name, clipnorm=clipnorm, clipvalue=clipvalue, global_clipnorm=global_clipnorm, use_ema=use_ema, ema_momentum=ema_momentum, ema_overwrite_frequency=ema_overwrite_frequency, jit_compile=jit_compile, **kwargs ) self._learning_rate = self._build_learning_rate(learning_rate) self.beta_1 = beta_1 self.beta_2 = beta_2 self.epsilon = epsilon self.amsgrad = amsgrad def build(self, var_list): """Initialize optimizer variables. Adam optimizer has 3 types of variables: momentums, velocities and velocity_hat (only set when amsgrad is applied), Args: var_list: list of model variables to build Adam variables on. """ super().build(var_list) if hasattr(self, "_built") and self._built: return self._built = True self._momentums = [] self._velocities = [] for var in var_list: self._momentums.append( self.add_variable_from_reference( model_variable=var, variable_name="m" ) ) self._velocities.append( self.add_variable_from_reference( model_variable=var, variable_name="v" ) ) if self.amsgrad: self._velocity_hats = [] for var in var_list: self._velocity_hats.append( self.add_variable_from_reference( model_variable=var, variable_name="vhat" ) ) def update_step(self, gradient, variable): """Update step given gradient and the associated model variable.""" beta_1_power = None beta_2_power = None lr = tf.cast(self.learning_rate, variable.dtype) local_step = tf.cast(self.iterations + 1, variable.dtype) beta_1_power = tf.pow(tf.cast(self.beta_1, variable.dtype), local_step) beta_2_power = tf.pow(tf.cast(self.beta_2, variable.dtype), local_step) var_key = self._var_key(variable) m = self._momentums[self._index_dict[var_key]] v = self._velocities[self._index_dict[var_key]] alpha = lr * tf.sqrt(1 - beta_2_power) / (1 - beta_1_power) if isinstance(gradient, tf.IndexedSlices): # Sparse gradients. m.assign_add(-m * (1 - self.beta_1)) m.scatter_add( tf.IndexedSlices( gradient.values * (1 - self.beta_1), gradient.indices ) ) v.assign_add(-v * (1 - self.beta_2)) v.scatter_add( tf.IndexedSlices( tf.square(gradient.values) * (1 - self.beta_2), gradient.indices, ) ) if self.amsgrad: v_hat = self._velocity_hats[self._index_dict[var_key]] v_hat.assign(tf.maximum(v_hat, v)) v = v_hat variable.assign_sub((m * alpha) / (tf.sqrt(v) + self.epsilon)) else: # Dense gradients. m.assign_add((gradient - m) * (1 - self.beta_1)) v.assign_add((tf.square(gradient) - v) * (1 - self.beta_2)) if self.amsgrad: v_hat = self._velocity_hats[self._index_dict[var_key]] v_hat.assign(tf.maximum(v_hat, v)) v = v_hat variable.assign_sub((m * alpha) / (tf.sqrt(v) + self.epsilon)) def get_config(self): config = super().get_config() config.update( { "learning_rate": self._serialize_hyperparameter( self._learning_rate ), "beta_1": self.beta_1, "beta_2": self.beta_2, "epsilon": self.epsilon, "amsgrad": self.amsgrad, } ) return config Adam.__doc__ = Adam.__doc__.replace( "{{base_optimizer_keyword_args}}", optimizer.base_optimizer_keyword_args )