a 8Sic/ @sddlZddlmZddlmZmZddlmZmZGdddeZdeeeeeeee e e e e e e e d d d Z eeeeeeee e e e e e e d d d Z eeeeeeee e e e e e e d ddZ dS)N)Tensor) Optimizerrequired)ListOptionalcs\eZdZdZeddddfdddeedfddZfd d Ze d d d Z Z S)SGDaxImplements stochastic gradient descent (optionally with momentum). .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}, \: \lambda \text{ (weight decay)}, \\ &\hspace{13mm} \:\mu \text{ (momentum)}, \:\tau \text{ (dampening)}, \:\textit{ nesterov,}\:\textit{ maximize} \\[-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}\textbf{if} \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}\textbf{if} \: \mu \neq 0 \\ &\hspace{10mm}\textbf{if} \: t > 1 \\ &\hspace{15mm} \textbf{b}_t \leftarrow \mu \textbf{b}_{t-1} + (1-\tau) g_t \\ &\hspace{10mm}\textbf{else} \\ &\hspace{15mm} \textbf{b}_t \leftarrow g_t \\ &\hspace{10mm}\textbf{if} \: \textit{nesterov} \\ &\hspace{15mm} g_t \leftarrow g_{t} + \mu \textbf{b}_t \\ &\hspace{10mm}\textbf{else} \\[-1.ex] &\hspace{15mm} g_t \leftarrow \textbf{b}_t \\ &\hspace{5mm}\textbf{if} \: \textit{maximize} \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} + \gamma g_t \\[-1.ex] &\hspace{5mm}\textbf{else} \\[-1.ex] &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma g_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned} Nesterov momentum is based on the formula from `On the importance of initialization and momentum in deep learning`__. Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float): learning rate momentum (float, optional): momentum factor (default: 0) weight_decay (float, optional): weight decay (L2 penalty) (default: 0) dampening (float, optional): dampening for momentum (default: 0) nesterov (bool, optional): enables Nesterov momentum (default: False) maximize (bool, optional): maximize the params based on the objective, instead of minimizing (default: False) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) Example: >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9) >>> optimizer.zero_grad() >>> loss_fn(model(input), target).backward() >>> optimizer.step() __ http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf .. note:: The implementation of SGD with Momentum/Nesterov subtly differs from Sutskever et. al. and implementations in some other frameworks. Considering the specific case of Momentum, the update can be written as .. math:: \begin{aligned} v_{t+1} & = \mu * v_{t} + g_{t+1}, \\ p_{t+1} & = p_{t} - \text{lr} * v_{t+1}, \end{aligned} where :math:`p`, :math:`g`, :math:`v` and :math:`\mu` denote the parameters, gradient, velocity, and momentum respectively. This is in contrast to Sutskever et. al. and other frameworks which employ an update of the form .. math:: \begin{aligned} v_{t+1} & = \mu * v_{t} + \text{lr} * g_{t+1}, \\ p_{t+1} & = p_{t} - v_{t+1}. \end{aligned} The Nesterov version is analogously modified. rFN)maximizeforeach)r c s|tur|dkrtd||dkr4td||dkrJtd|t|||||||d} |r||dkst|dkr|tdtt||| dS)NgzInvalid learning rate: {}zInvalid momentum value: {}zInvalid weight_decay value: {})lrmomentum dampening weight_decaynesterovr r rz8Nesterov momentum requires a momentum and zero dampening)r ValueErrorformatdictsuperr__init__) selfparamsr r r rrr r defaults __class__K/var/www/html/django/DPS/env/lib/python3.9/site-packages/torch/optim/sgd.pyr[sz SGD.__init__cs@t||jD](}|dd|dd|ddqdS)NrFr r )r __setstate__ param_groups setdefault)rstategrouprrrrks     zSGD.__setstate__c Cs d}|dur:t|}Wdn1s00Y|jD]}g}g}g}d}|dD]\}|jdur\||||j|jjrd}|j|} d| vr|dq\|| dq\t||||d|d|d|d |d |d ||d d t||D]\}} |j|} | | d<qq@|S)zPerforms a single optimization step. Args: closure (callable, optional): A closure that reevaluates the model and returns the loss. NFrTmomentum_bufferrr r r rr r )rr r r rr has_sparse_gradr ) torch enable_gradrgradappend is_sparsersgdzip) rclosurelossr params_with_gradd_p_listmomentum_buffer_listr"prr!rrrsteprsF $          zSGD.step)N) __name__ __module__ __qualname____doc__rrboolrrr#no_gradr0 __classcell__rrrrrsS r) rr-r.r"r rr r r rr c CsZ|dur d}|r"tjr"td|r6tjs6t} nt} | |||||||| || d dS)zlFunctional API that performs SGD algorithm computation. See :class:`~torch.optim.SGD` for details. 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