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# 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

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)

def step(self, closure=None):
"""Performs a single optimization step.

Args:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()

for group in self.param_groups:
square_avgs = []
momentum_buffer_list = []

for p in group['params']:
continue

raise RuntimeError('RMSprop does not support sparse gradients')

state = self.state[p]

# State initialization
if len(state) == 0:
state['step'] = 0
state['square_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
if group['momentum'] > 0:
state['momentum_buffer'] = torch.zeros_like(p, memory_format=torch.preserve_format)
if group['centered']:

square_avgs.append(state['square_avg'])

if group['momentum'] > 0:
momentum_buffer_list.append(state['momentum_buffer'])
if group['centered']:

state['step'] += 1

square_avgs,
momentum_buffer_list,
lr=group['lr'],
alpha=group['alpha'],
eps=group['eps'],
weight_decay=group['weight_decay'],
momentum=group['momentum'],
centered=group['centered'])

return loss


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