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from .optimizer import Optimizer, required
class SGD(Optimizer):
r"""Implements stochastic gradient descent (optionally with momentum).
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)
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::
v = \rho * v + g \\
p = p - lr * v
where p, g, v and :math:`\rho` denote the parameters, gradient, velocity, and
momentum respectively.
This is in constrast to Sutskever et. al. and
other frameworks which employ an update of the form
.. math::
v = \rho * v + lr * g \\
p = p - v
The Nesterov version is analogously modified.
"""
def __init__(self, params, lr=required, momentum=0, dampening=0,
weight_decay=0, nesterov=False):
defaults = dict(lr=lr, momentum=momentum, dampening=dampening,
weight_decay=weight_decay, nesterov=nesterov)
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(SGD, self).__setstate__(state)
for group in self.param_groups:
group.setdefault('nesterov', False)
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
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:
weight_decay = group['weight_decay']
momentum = group['momentum']
dampening = group['dampening']
nesterov = group['nesterov']
for p in group['params']:
if p.grad is None:
continue
d_p = p.grad.data
if weight_decay != 0:
d_p.add_(weight_decay, p.data)
if momentum != 0:
param_state = self.state[p]
if 'momentum_buffer' not in param_state:
buf = param_state['momentum_buffer'] = d_p.clone()
else:
buf = param_state['momentum_buffer']
buf.mul_(momentum).add_(1 - dampening, d_p)
if nesterov:
d_p = d_p.add(momentum, buf)
else:
d_p = buf
p.data.add_(-group['lr'], d_p)
return loss
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