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