U <c=6@sddlZddlmZddlmZmZddlmZmZddgZGdddeZ deeeeeeeeeee e e e e e e e e d d dZ eeeeeeeeeee e e e e e e e d d dZ eeeeeeeeeee e e e e e e e d ddZdS)N)Tensor) Optimizer_use_grad_for_differentiable)ListOptionalRMSproprmspropc sJeZdZdZdeeeedfd d Zfd d Zedd dZ Z S)raImplements RMSprop algorithm. .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \alpha \text{ (alpha)},\: \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)} \\ &\hspace{13mm} \lambda \text{ (weight decay)},\: \mu \text{ (momentum)},\: centered\\ &\textbf{initialize} : v_0 \leftarrow 0 \text{ (square average)}, \: \textbf{b}_0 \leftarrow 0 \text{ (buffer)}, \: g^{ave}_0 \leftarrow 0 \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}if \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}v_t \leftarrow \alpha v_{t-1} + (1 - \alpha) g^2_t \hspace{8mm} \\ &\hspace{5mm} \tilde{v_t} \leftarrow v_t \\ &\hspace{5mm}if \: centered \\ &\hspace{10mm} g^{ave}_t \leftarrow g^{ave}_{t-1} \alpha + (1-\alpha) g_t \\ &\hspace{10mm} \tilde{v_t} \leftarrow \tilde{v_t} - \big(g^{ave}_{t} \big)^2 \\ &\hspace{5mm}if \: \mu > 0 \\ &\hspace{10mm} \textbf{b}_t\leftarrow \mu \textbf{b}_{t-1} + g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big) \\ &\hspace{10mm} \theta_t \leftarrow \theta_{t-1} - \gamma \textbf{b}_t \\ &\hspace{5mm} else \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big) \hspace{3mm} \\ &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned} For further details regarding the algorithm we refer to `lecture notes `_ by G. Hinton. and centered version `Generating Sequences With Recurrent Neural Networks `_. The implementation here takes the square root of the gradient average before adding epsilon (note that TensorFlow interchanges these two operations). The effective learning rate is thus :math:`\gamma/(\sqrt{v} + \epsilon)` where :math:`\gamma` is the scheduled learning rate and :math:`v` is the weighted moving average of the squared gradient. Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 1e-2) momentum (float, optional): momentum factor (default: 0) alpha (float, optional): smoothing constant (default: 0.99) eps (float, optional): term added to the denominator to improve numerical stability (default: 1e-8) centered (bool, optional) : if ``True``, compute the centered RMSProp, the gradient is normalized by an estimation of its variance weight_decay (float, optional): weight decay (L2 penalty) (default: 0) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) maximize (bool, optional): maximize the params based on the objective, instead of minimizing (default: False) {Gz?Gz?:0yE>rFN)foreachmaximizedifferentiablec sd|kstd|d|ks,td|d|ksBtd|d|ksXtd|d|ksntd|t|||||||| | d } tt||| dS)NgzInvalid learning rate: {}zInvalid epsilon value: {}zInvalid momentum value: {}zInvalid weight_decay value: {}zInvalid alpha value: {}) lrmomentumalphaepscentered weight_decayr rr) ValueErrorformatdictsuperr__init__) selfparamsrrrrrrr rrdefaults __class__7/tmp/pip-unpacked-wheel-gikjz4vx/torch/optim/rmsprop.pyrFs" zRMSprop.__init__csXt||jD]@}|dd|dd|dd|dd|ddqdS)NrrrFr rr)r __setstate__ param_groups setdefault)rstategrouprr r!r"Ys      zRMSprop.__setstate__c Csd}|dk r&t |}W5QRX|jD]}g}g}g}g}g}|dD]} | jdkr`qN|| | jjrztd|| j|j| } t| dkrd| d<tj | tj d| d<|ddkrtj | tj d| d <|d rtj | tj d| d <|| d|ddkr|| d |d r6|| d |d rXt | dt rXtd | dd7<qNt ||||||d|d|d|d|d|d |d|d|d dq,|S)zPerforms a single optimization step. Args: closure (Callable, optional): A closure that reevaluates the model and returns the loss. Nrz)RMSprop does not support sparse gradientsrstep)Z memory_format square_avgrZmomentum_bufferrgrad_avgrz`step` can't be a tensorrrrrrr r) rrrrrrr rr)torchZ enable_gradr#gradappendZ is_sparse RuntimeErrorr%lenZ zeros_likeZpreserve_format isinstancerr ) rclosureZlossr&Zparams_with_gradgrads square_avgs grad_avgsmomentum_buffer_listpr%r r r!r'bsb         z RMSprop.step) r r r rrFNFF)N) __name__ __module__ __qualname____doc__rboolrr"rr' __classcell__r r rr!rs= F)rr1r2r3r4r rrrrrrrrcCs`|dkr d}|r"tjr"td|r6tjs6t}nt}|||||||| | | | | ||d dS)zsFunctional API that performs rmsprop algorithm computation. See :class:`~torch.optim.RMSProp` for details. 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