# 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. # ============================================================================== """Adadelta optimizer implementation.""" # pylint: disable=g-classes-have-attributes from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np from tensorflow.python.framework import ops from tensorflow.python.keras import backend_config from tensorflow.python.keras.optimizer_v2 import optimizer_v2 from tensorflow.python.ops import array_ops from tensorflow.python.training import gen_training_ops from tensorflow.python.util.tf_export import keras_export @keras_export('keras.optimizers.Adadelta') 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, initial learning rate can be set, as in most other Keras optimizers. According to section 4.3 ("Effective Learning rates"), near the end of training step sizes converge to 1 which is effectively a high learning rate which would cause divergence. This occurs only near the end of the training as gradients and step sizes are small, and the epsilon constant in the numerator and denominator dominate past gradients and parameter updates which converge the learning rate to 1. According to section 4.4("Speech Data"),where a large neural network with 4 hidden layers was trained on a corpus of US English data, ADADELTA was used with 100 network replicas.The epsilon used is 1e-6 with rho=0.95 which converged faster than ADAGRAD, by the following construction: def __init__(self, lr=1.0, rho=0.95, epsilon=1e-6, decay=0., **kwargs): Args: learning_rate: A `Tensor`, floating point value, or a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`. The learning rate. To match the exact form in the original paper use 1.0. rho: A `Tensor` or a floating point value. The decay rate. epsilon: A `Tensor` or a floating point value. A constant epsilon used to better conditioning the grad update. 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; `"clipvalue"` (float) clips gradients by value. 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=ops.convert_to_tensor_v2_with_dispatch( self.epsilon, var_dtype), rho=array_ops.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 gen_training_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 gen_training_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._serialize_hyperparameter('decay'), 'rho': self._serialize_hyperparameter('rho'), 'epsilon': self.epsilon, }) return config