SGD — PyTorch 2.0 documentation (original) (raw)

class torch.optim.SGD(params, lr=, momentum=0, dampening=0, weight_decay=0, nesterov=False, *, maximize=False, foreach=None, differentiable=False)[source]

Implements stochastic gradient descent (optionally with momentum).

input:γ (lr), θ0 (params), f(θ) (objective), λ (weight decay), μ (momentum), τ (dampening), nesterov, maximizefor t=1 to … dogt←∇θft(θt−1)if λ≠0gt←gt+λθt−1if μ≠0if t>1bt←μbt−1+(1−τ)gtelsebt←gtif nesterovgt←gt+μbtelsegt←btif maximizeθt←θt−1+γgtelseθt←θt−1−γgtreturn θt\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 fromOn the importance of initialization and momentum in deep learning.

Parameters:

Example

optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9) optimizer.zero_grad() loss_fn(model(input), target).backward() optimizer.step()

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

vt+1=μ∗vt+gt+1,pt+1=pt−lr∗vt+1,\begin{aligned} v_{t+1} & = \mu * v_{t} + g_{t+1}, \\ p_{t+1} & = p_{t} - \text{lr} * v_{t+1}, \end{aligned}

where pp, gg, vv and μ\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

vt+1=μ∗vt+lr∗gt+1,pt+1=pt−vt+1.\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.

Moreover, the initial value of the momentum buffer is set to the gradient value at the first step. This is in contrast to some other frameworks that initialize it to all zeros.

add_param_group(param_group)

Add a param group to the Optimizer s param_groups.

This can be useful when fine tuning a pre-trained network as frozen layers can be made trainable and added to the Optimizer as training progresses.

Parameters:

param_group (dict) – Specifies what Tensors should be optimized along with group specific optimization options.

load_state_dict(state_dict)

Loads the optimizer state.

Parameters:

state_dict (dict) – optimizer state. Should be an object returned from a call to state_dict().

register_step_post_hook(hook)

Register an optimizer step post hook which will be called after optimizer step. It should have the following signature:

hook(optimizer, args, kwargs) -> None

The optimizer argument is the optimizer instance being used.

Parameters:

hook (Callable) – The user defined hook to be registered.

Returns:

a handle that can be used to remove the added hook by callinghandle.remove()

Return type:

torch.utils.hooks.RemoveableHandle

register_step_pre_hook(hook)

Register an optimizer step pre hook which will be called before optimizer step. It should have the following signature:

hook(optimizer, args, kwargs) -> None or modified args and kwargs

The optimizer argument is the optimizer instance being used. If args and kwargs are modified by the pre-hook, then the transformed values are returned as a tuple containing the new_args and new_kwargs.

Parameters:

hook (Callable) – The user defined hook to be registered.

Returns:

a handle that can be used to remove the added hook by callinghandle.remove()

Return type:

torch.utils.hooks.RemoveableHandle

state_dict()

Returns the state of the optimizer as a dict.

It contains two entries:

zero_grad(set_to_none=True)

Sets the gradients of all optimized torch.Tensor s to zero.

Parameters:

set_to_none (bool) – instead of setting to zero, set the grads to None. This will in general have lower memory footprint, and can modestly improve performance. However, it changes certain behaviors. For example: 1. When the user tries to access a gradient and perform manual ops on it, a None attribute or a Tensor full of 0s will behave differently. 2. If the user requests zero_grad(set_to_none=True) followed by a backward pass, .grads are guaranteed to be None for params that did not receive a gradient. 3. torch.optim optimizers have a different behavior if the gradient is 0 or None (in one case it does the step with a gradient of 0 and in the other it skips the step altogether).