/usr/local/lib64/python3.6/site-packages/torch/optim/__pycache__
Edit: /usr/local/lib64/python3.6/site-packages/torch/optim/__pycache__/sgd.cpython-36.pyc (6267B)
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S ) SGDa 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)},\:nesterov\\[-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} \: nesterov \\
&\hspace{15mm} g_t \leftarrow g_{t-1} + \mu \textbf{b}_t \\
&\hspace{10mm}\textbf{else} \\[-1.ex]
&\hspace{15mm} g_t \leftarrow \textbf{b}_t \\
&\hspace{5mm}\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)
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::
\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.
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