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.

## Usage

optim_sgd(
params,
lr = optim_required(),
momentum = 0,
dampening = 0,
weight_decay = 0,
nesterov = FALSE
)

## Arguments

params

(iterable): iterable of parameters to optimize or dicts defining parameter groups

lr

(float): learning rate

momentum

(float, optional): momentum factor (default: 0)

dampening

(float, optional): dampening for momentum (default: 0)

weight_decay

(float, optional): weight decay (L2 penalty) (default: 0)

nesterov

(bool, optional): enables Nesterov momentum (default: FALSE)

## 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 $$\begin{array}{ll} v_{t+1} & = \mu * v_{t} + g_{t+1}, \\ p_{t+1} & = p_{t} - \mbox{lr} * v_{t+1}, \end{array}$$

where $$p$$, $$g$$, $$v$$ and $$\mu$$ 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

$$\begin{array}{ll} v_{t+1} & = \mu * v_{t} + \mbox{lr} * g_{t+1}, \\ p_{t+1} & = p_{t} - v_{t+1}. \end{array}$$ The Nesterov version is analogously modified.

## Warning

If you need to move a model to GPU via $cuda(), please do so before constructing optimizers for it. Parameters of a model after $cuda() will be different objects from those before the call. In general, you should make sure that the objects pointed to by model parameters subject to optimization remain the same over the whole lifecycle of optimizer creation and usage.

## Examples

if (torch_is_installed()) {
if (FALSE) {
optimizer <- optim_sgd(model$parameters(), lr = 0.1, momentum = 0.9) optimizer$zero_grad()
loss_fn(model(input), target)$backward() optimizer$step()
}

}