Source code for torch.optim.rmsprop
import torch
from torch import Tensor
from .optimizer import Optimizer
from typing import List, Optional
[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)
foreach (bool, optional): whether foreach implementation of optimizer
is used (default: None)
"""
def __init__(self, params, lr=1e-2, alpha=0.99, eps=1e-8, weight_decay=0, momentum=0,
centered=False, foreach: Optional[bool] = None):
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, foreach=foreach)
super(RMSprop, self).__init__(params, defaults)
def __setstate__(self, state):
super().__setstate__(state)
for group in self.param_groups:
group.setdefault('momentum', 0)
group.setdefault('centered', False)
group.setdefault('foreach', None)
[docs] @torch.no_grad()
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:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
params_with_grad = []
grads = []
square_avgs = []
grad_avgs = []
momentum_buffer_list = []
for p in group['params']:
if p.grad is None:
continue
params_with_grad.append(p)
if p.grad.is_sparse:
raise RuntimeError('RMSprop does not support sparse gradients')
grads.append(p.grad)
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']:
state['grad_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
square_avgs.append(state['square_avg'])
if group['momentum'] > 0:
momentum_buffer_list.append(state['momentum_buffer'])
if group['centered']:
grad_avgs.append(state['grad_avg'])
state['step'] += 1
rmsprop(params_with_grad,
grads,
square_avgs,
grad_avgs,
momentum_buffer_list,
lr=group['lr'],
alpha=group['alpha'],
eps=group['eps'],
weight_decay=group['weight_decay'],
momentum=group['momentum'],
centered=group['centered'],
foreach=group['foreach'])
return loss
def rmsprop(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
grad_avgs: List[Tensor],
momentum_buffer_list: List[Tensor],
# kwonly args with defaults are not supported by functions compiled with torchscript issue #70627
# setting this as kwarg for now as functional API is compiled by torch/distributed/optim
foreach: bool = None,
*,
lr: float,
alpha: float,
eps: float,
weight_decay: float,
momentum: float,
centered: bool):
r"""Functional API that performs rmsprop algorithm computation.
See :class:`~torch.optim.RMSProp` for details.
"""
if foreach is None:
# Placeholder for more complex foreach logic to be added when value is not set
foreach = False
if foreach and torch.jit.is_scripting():
raise RuntimeError('torch.jit.script not supported with foreach optimizers')
if foreach and not torch.jit.is_scripting():
func = _multi_tensor_rmsprop
else:
func = _single_tensor_rmsprop
func(params,
grads,
square_avgs,
grad_avgs,
momentum_buffer_list,
lr=lr,
alpha=alpha,
eps=eps,
weight_decay=weight_decay,
momentum=momentum,
centered=centered)
def _single_tensor_rmsprop(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
grad_avgs: List[Tensor],
momentum_buffer_list: List[Tensor],
*,
lr: float,
alpha: float,
eps: float,
weight_decay: float,
momentum: float,
centered: bool):
for i, param in enumerate(params):
grad = grads[i]
square_avg = square_avgs[i]
if weight_decay != 0:
grad = grad.add(param, alpha=weight_decay)
square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha)
if centered:
grad_avg = grad_avgs[i]
grad_avg.mul_(alpha).add_(grad, alpha=1 - alpha)
avg = square_avg.addcmul(grad_avg, grad_avg, value=-1).sqrt_().add_(eps)
else:
avg = square_avg.sqrt().add_(eps)
if momentum > 0:
buf = momentum_buffer_list[i]
buf.mul_(momentum).addcdiv_(grad, avg)
param.add_(buf, alpha=-lr)
else:
param.addcdiv_(grad, avg, value=-lr)
def _multi_tensor_rmsprop(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
grad_avgs: List[Tensor],
momentum_buffer_list: List[Tensor],
*,
lr: float,
alpha: float,
eps: float,
weight_decay: float,
momentum: float,
centered: bool):
if len(params) == 0:
return
if weight_decay != 0:
torch._foreach_add_(grads, params, alpha=weight_decay)
torch._foreach_mul_(square_avgs, alpha)
torch._foreach_addcmul_(square_avgs, grads, grads, value=1 - alpha)
if centered:
torch._foreach_mul_(grad_avgs, alpha)
torch._foreach_add_(grad_avgs, grads, alpha=1 - alpha)
avg = torch._foreach_addcmul(square_avgs, grad_avgs, grad_avgs, value=-1)
torch._foreach_sqrt_(avg)
torch._foreach_add_(avg, eps)
else:
avg = torch._foreach_sqrt(square_avgs)
torch._foreach_add_(avg, eps)
if momentum > 0:
torch._foreach_mul_(momentum_buffer_list, momentum)
torch._foreach_addcdiv_(momentum_buffer_list, grads, avg)
torch._foreach_add_(params, momentum_buffer_list, alpha=-lr)
else:
torch._foreach_addcdiv_(params, grads, avg, value=-lr)
