Shortcuts

# Source code for torch.optim.rmsprop

import torch
from . import _functional as F
from .optimizer import Optimizer

[docs]class RMSprop(Optimizer): r"""Implements 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 <https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf>_ by G. Hinton. and centered version Generating Sequences With Recurrent Neural Networks <https://arxiv.org/pdf/1308.0850v5.pdf>_. 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) """ def __init__(self, params, lr=1e-2, alpha=0.99, eps=1e-8, weight_decay=0, momentum=0, centered=False): if not 0.0 <= lr: raise ValueError("Invalid learning rate: {}".format(lr)) if not 0.0 <= eps: raise ValueError("Invalid epsilon value: {}".format(eps)) if not 0.0 <= momentum: raise ValueError("Invalid momentum value: {}".format(momentum)) if not 0.0 <= weight_decay: raise ValueError("Invalid weight_decay value: {}".format(weight_decay)) if not 0.0 <= alpha: raise ValueError("Invalid alpha value: {}".format(alpha)) defaults = dict(lr=lr, momentum=momentum, alpha=alpha, eps=eps, centered=centered, weight_decay=weight_decay) super(RMSprop, self).__init__(params, defaults) def __setstate__(self, state): super(RMSprop, self).__setstate__(state) for group in self.param_groups: group.setdefault('momentum', 0) group.setdefault('centered', False)

## Docs

Access comprehensive developer documentation for PyTorch

View Docs

## Tutorials

Get in-depth tutorials for beginners and advanced developers

View Tutorials