# Copyright (c) 2020 PaddlePaddle 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. from .optimizer import Optimizer from ..fluid import core from ..fluid import framework from ..fluid.framework import Variable __all__ = ["RMSProp"] class RMSProp(Optimizer): """ Root Mean Squared Propagation (RMSProp) is an unpublished, adaptive learning rate method. The original slides proposed RMSProp: Slide 29 of http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf . The original equation is as follows: .. math:: r(w, t) & = \\rho r(w, t-1) + (1 - \\rho)(\\nabla Q_{i}(w))^2 w & = w - \\frac{\\eta} {\\sqrt{r(w,t) + \\epsilon}} \\nabla Q_{i}(w) The first equation calculates moving average of the squared gradient for each weight. Then dividing the gradient by :math:`sqrt{v(w,t)}`. In some cases, adding a momentum term :math: `\\beta` is beneficial. In our implementation, Nesterov momentum is used: .. math:: r(w, t) & = \\rho r(w, t-1) + (1 - \\rho)(\\nabla Q_{i}(w))^2 v(w, t) & = \\beta v(w, t-1) + \\frac{\\eta} {\\sqrt{r(w,t) + \\epsilon}} \\nabla Q_{i}(w) w & = w - v(w, t) if centered is True: .. math:: r(w, t) & = \\rho r(w, t-1) + (1 - \\rho)(\\nabla Q_{i}(w))^2 g(w, t) & = \\rho g(w, t-1) + (1 - \\rho)\\nabla Q_{i}(w) v(w, t) & = \\beta v(w, t-1) + \\frac{\\eta} {\\sqrt{r(w,t) - (g(w, t))^2 + \\epsilon}} \\nabla Q_{i}(w) w & = w - v(w, t) where, :math:`\\rho` is a hyperparameter and typical values are 0.9, 0.95 and so on. :math: `beta` is the momentum term. :math: `\\epsilon` is a smoothing term to avoid division by zero, usually set somewhere in range from 1e-4 to 1e-8. Parameters: learning_rate (float|_LRScheduler): The learning rate used to update ``Parameter``. It can be a float value or a _LRScheduler. rho(float): rho is :math: `\\rho` in equation, default is 0.95. epsilon(float): :math: `\\epsilon` in equation is smoothing term to avoid division by zero, default is 1e-6. momentum(float): :math:`\\beta` in equation is the momentum term, default is 0.0. centered(bool): If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False. parameters (list, optional): List of ``Tensor`` to update to minimize ``loss``. \ This parameter is required in dygraph mode. \ The default value is None in static mode, at this time all parameters will be updated. weight_decay (float|WeightDecayRegularizer, optional): The strategy of regularization. \ It canbe a float value as coeff of L2 regularization or \ :ref:`api_fluid_regularizer_L1Decay`, :ref:`api_fluid_regularizer_L2Decay`. If a parameter has set regularizer using :ref:`api_fluid_ParamAttr` already, \ the regularization setting here in optimizer will be ignored for this parameter. \ Otherwise, the regularization setting here in optimizer will take effect. \ Default None, meaning there is no regularization. grad_clip (GradientClipBase, optional): Gradient cliping strategy, it's an instance of some derived class of ``GradientClipBase`` . There are three cliping strategies ( :ref:`api_fluid_clip_GradientClipByGlobalNorm` , :ref:`api_fluid_clip_GradientClipByNorm` , :ref:`api_fluid_clip_GradientClipByValue` ). Default None, meaning there is no gradient clipping. name (str, optional): This parameter is used by developers to print debugging information. \ For details, please refer to :ref:`api_guide_Name`. Default is None. Raises: ValueError: If learning_rate, rho, epsilon, momentum are None. Examples: .. code-block:: python import paddle inp = paddle.rand([10,10], dtype="float32") linear = paddle.nn.Linear(10, 10) out = linear(inp) loss = paddle.mean(out) rmsprop = paddle.optimizer.RMSProp(learning_rate=0.1, parameters=linear.parameters(), weight_decay=0.01) out.backward() rmsprop.step() rmsprop.clear_grad() """ _momentum_acc_str = "momentum" _mean_square_acc_str = "mean_square" _mean_grad_acc_str = "mean_grad" def __init__(self, learning_rate, rho=0.95, epsilon=1.0e-6, momentum=0.0, centered=False, parameters=None, weight_decay=None, grad_clip=None, name=None): if learning_rate is None: raise ValueError("learning_rate is not set.") if rho is None: raise ValueError("rho is not set.") if epsilon is None: raise ValueError("epsilon is not set.") if momentum is None: raise ValueError("momentum is not set.") if not 0.0 <= epsilon: raise ValueError("Invalid value of epsilon, expect epsilon >= 0.") if not 0.0 <= momentum: raise ValueError("Invalid value of momentum, expect momentum >= 0.") if not 0.0 <= rho: raise ValueError("Invalid value of rho, expect rho >= 0.") super(RMSProp, self).__init__( learning_rate=learning_rate, parameters=parameters, weight_decay=weight_decay, grad_clip=grad_clip, name=name) self.type = "rmsprop" self._rho = rho self._epsilon = epsilon self._momentum = momentum self._centered = centered def _create_accumulators(self, block, parameters): if not isinstance(block, framework.Block): raise TypeError("block is not instance of framework.Block.") for p in parameters: self._add_accumulator(self._momentum_acc_str, p) self._add_accumulator(self._mean_square_acc_str, p) self._add_accumulator(self._mean_grad_acc_str, p) def _append_optimize_op(self, block, param_and_grad): if not isinstance(block, framework.Block): raise TypeError("block is not instance of framework.Block.") momentum_acc = self._get_accumulator(self._momentum_acc_str, param_and_grad[0]) mean_square_acc = self._get_accumulator(self._mean_square_acc_str, param_and_grad[0]) mean_grad_acc = self._get_accumulator(self._mean_grad_acc_str, param_and_grad[0]) rmsprop_op = block.append_op( type=self.type, inputs={ "Param": param_and_grad[0], "Grad": param_and_grad[1], "Moment": momentum_acc, "MeanSquare": mean_square_acc, "MeanGrad": mean_grad_acc, "LearningRate": self._create_param_lr(param_and_grad), }, outputs={ "ParamOut": param_and_grad[0], "MomentOut": momentum_acc, "MeanSquareOut": mean_square_acc, "MeanGradOut": mean_grad_acc }, attrs={ "epsilon": self._epsilon, "decay": self._rho, "momentum": self._momentum, "centered": self._centered }, stop_gradient=True) return rmsprop_op