U d .@sddlZddlmZddlmZddlmZmZGdddeZdeeeeeeeeeeee e e e e ed d d Z eeeeeeeeeee e e e e ed d d Z eeeeeeeeeee e e e e ed ddZ dS)N)Tensor) Optimizer)ListOptionalcsJeZdZdZdeedfd d Zfd d Ze dd dZ Z S)RMSpropaImplements 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) {Gz?Gz?:0yE>rFN)foreachc 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 ) ValueErrorformatdictsuperr__init__) selfparamsr rrrr rr defaults __class__7/tmp/pip-unpacked-wheel-ua33x9lu/torch/optim/rmsprop.pyrCs zRMSprop.__init__cs@t||jD](}|dd|dd|ddqdS)Nr rrFr )r __setstate__ param_groups setdefault)rstategrouprrrrTs     zRMSprop.__setstate__c Csd}|dk r&t |}W5QRX|jD]T}g}g}g}g}g}|dD]} | jdkr^qN|| | jjrxtd|| j|j| } t| dkrd| d<tj | tj d| d<|ddkrtj | tj d| d <|d rtj | tj d| d <|| d|ddkr|| d |d r4|| d | dd 7<qNt ||||||d |d|d|d|d|d |dd q,|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_avgr Zmomentum_bufferrgrad_avgrr rrrr )r rrrr rr ) torchZ enable_gradrgradappendZ is_sparse RuntimeErrorr!lenZ zeros_likeZpreserve_formatrmsprop) rclosureZlossr"Zparams_with_gradgrads square_avgs grad_avgsmomentum_buffer_listpr!rrrr#[sZ           z RMSprop.step)rr r rrFN)N) __name__ __module__ __qualname____doc__rboolrrr&Zno_gradr# __classcell__rrrrrs; r) rr-r.r/r0r r rrrr rc Cs\|dkr d}|r"tjr"td|r6tjs6t} nt} | ||||||||| | | d dS)zsFunctional API that performs rmsprop algorithm computation. See :class:`~torch.optim.RMSProp` for details. NFz6torch.jit.script not supported with foreach optimizers)r rrrr r)r&ZjitZ is_scriptingr)_multi_tensor_rmsprop_single_tensor_rmsprop) rr-r.r/r0r r rrrr rfuncrrrr+s&r+) rr-r.r/r0r rrrr rcCst|D]\} } || } || }|dkr6| j| |d} ||j| | d|d| r|| }||j| d|d|j||dd|}n||}| dkr|| }|| | || j|| dq| j| || dqdSNr)rr)value) enumerateaddZmul_Zaddcmul_Zadd_ZaddcmulZsqrt_sqrtZaddcdiv_)rr-r.r/r0r rrrr riparamr'r$r%avgbufrrrr9s r9c Cst|dkrdS|dkr(tj|||dt||tj|||d|d| rt||tj||d|dtj|||dd} t| t| |nt|} t| || dkrt|| t||| tj||| dntj||| | ddSr;) r*r&Z _foreach_add_Z _foreach_mul_Z_foreach_addcmul_Z_foreach_addcmulZ_foreach_sqrt_Z _foreach_sqrtZ_foreach_addcdiv_) rr-r.r/r0r rrrr rrCrrrr8s&       r8)N) r&rZ optimizerrtypingrrrr6floatr+r9r8rrrrsV   , %