Source code for torch.optim.sgd
import torch
from torch import Tensor
from .optimizer import Optimizer, required, _use_grad_for_differentiable
from typing import List, Optional
__all__ = ['SGD', 'sgd']
[docs]class SGD(Optimizer):
r"""Implements 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:
>>> # xdoctest: +SKIP
>>> 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.
"""
def __init__(self, params, lr=required, momentum=0, dampening=0,
weight_decay=0, nesterov=False, *, maximize=False, foreach: Optional[bool] = None,
differentiable=False):
if lr is not required and lr < 0.0:
raise ValueError("Invalid learning rate: {}".format(lr))
if momentum < 0.0:
raise ValueError("Invalid momentum value: {}".format(momentum))
if weight_decay < 0.0:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, momentum=momentum, dampening=dampening,
weight_decay=weight_decay, nesterov=nesterov,
maximize=maximize, foreach=foreach,
differentiable=differentiable)
if nesterov and (momentum <= 0 or dampening != 0):
raise ValueError("Nesterov momentum requires a momentum and zero dampening")
super(SGD, self).__init__(params, defaults)
def __setstate__(self, state):
super().__setstate__(state)
for group in self.param_groups:
group.setdefault('nesterov', False)
group.setdefault('maximize', False)
group.setdefault('foreach', None)
group.setdefault('differentiable', False)
@_use_grad_for_differentiable
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 = []
d_p_list = []
momentum_buffer_list = []
has_sparse_grad = False
for p in group['params']:
if p.grad is not None:
params_with_grad.append(p)
d_p_list.append(p.grad)
if p.grad.is_sparse:
has_sparse_grad = True
state = self.state[p]
if 'momentum_buffer' not in state:
momentum_buffer_list.append(None)
else:
momentum_buffer_list.append(state['momentum_buffer'])
sgd(params_with_grad,
d_p_list,
momentum_buffer_list,
weight_decay=group['weight_decay'],
momentum=group['momentum'],
lr=group['lr'],
dampening=group['dampening'],
nesterov=group['nesterov'],
maximize=group['maximize'],
has_sparse_grad=has_sparse_grad,
foreach=group['foreach'])
# update momentum_buffers in state
for p, momentum_buffer in zip(params_with_grad, momentum_buffer_list):
state = self.state[p]
state['momentum_buffer'] = momentum_buffer
return loss
def sgd(params: List[Tensor],
d_p_list: List[Tensor],
momentum_buffer_list: List[Optional[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
has_sparse_grad: bool = None,
foreach: bool = None,
*,
weight_decay: float,
momentum: float,
lr: float,
dampening: float,
nesterov: bool,
maximize: bool):
r"""Functional API that performs SGD algorithm computation.
See :class:`~torch.optim.SGD` 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_sgd
else:
func = _single_tensor_sgd
func(params,
d_p_list,
momentum_buffer_list,
weight_decay=weight_decay,
momentum=momentum,
lr=lr,
dampening=dampening,
nesterov=nesterov,
has_sparse_grad=has_sparse_grad,
maximize=maximize)
def _single_tensor_sgd(params: List[Tensor],
d_p_list: List[Tensor],
momentum_buffer_list: List[Optional[Tensor]],
*,
weight_decay: float,
momentum: float,
lr: float,
dampening: float,
nesterov: bool,
maximize: bool,
has_sparse_grad: bool):
for i, param in enumerate(params):
d_p = d_p_list[i] if not maximize else -d_p_list[i]
if weight_decay != 0:
d_p = d_p.add(param, alpha=weight_decay)
if momentum != 0:
buf = momentum_buffer_list[i]
if buf is None:
buf = torch.clone(d_p).detach()
momentum_buffer_list[i] = buf
else:
buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
if nesterov:
d_p = d_p.add(buf, alpha=momentum)
else:
d_p = buf
param.add_(d_p, alpha=-lr)
def _multi_tensor_sgd(params: List[Tensor],
grads: List[Tensor],
momentum_buffer_list: List[Optional[Tensor]],
*,
weight_decay: float,
momentum: float,
lr: float,
dampening: float,
nesterov: bool,
maximize: bool,
has_sparse_grad: bool):
if len(params) == 0:
return
if has_sparse_grad is None:
has_sparse_grad = any(grad.is_sparse for grad in grads)
if maximize:
grads = torch._foreach_neg(tuple(grads)) # type: ignore[assignment]
if weight_decay != 0:
grads = torch._foreach_add(grads, params, alpha=weight_decay)
if momentum != 0:
bufs = []
all_states_with_momentum_buffer = True
for i in range(len(momentum_buffer_list)):
if momentum_buffer_list[i] is None:
all_states_with_momentum_buffer = False
break
else:
bufs.append(momentum_buffer_list[i])
if all_states_with_momentum_buffer:
torch._foreach_mul_(bufs, momentum)
torch._foreach_add_(bufs, grads, alpha=1 - dampening)
else:
bufs = []
for i in range(len(momentum_buffer_list)):
if momentum_buffer_list[i] is None:
buf = momentum_buffer_list[i] = torch.clone(grads[i]).detach()
else:
buf = momentum_buffer_list[i]
buf.mul_(momentum).add_(grads[i], alpha=1 - dampening)
bufs.append(buf)
if nesterov:
torch._foreach_add_(grads, bufs, alpha=momentum)
else:
grads = bufs
if not has_sparse_grad:
torch._foreach_add_(params, grads, alpha=-lr)
else:
# foreach APIs dont support sparse
for i in range(len(params)):
params[i].add_(grads[i], alpha=-lr)
