Adam

class torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False, *, foreach=None, maximize=False, capturable=False, differentiable=False, fused=None)

Implements Adam algorithm.

$$\begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \beta_1, \beta_2 \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)} \\ &\hspace{13mm} \lambda \text{ (weight decay)}, \: \textit{amsgrad}, \:\textit{maximize} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, v_0\leftarrow 0 \text{ (second moment)},\: \widehat{v_0}^{max}\leftarrow 0\\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}\textbf{if} \: \textit{maximize}: \\ &\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}\textbf{if} \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ &\hspace{5mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\ &\hspace{5mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\ &\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\ &\hspace{5mm}\textbf{if} \: amsgrad \\ &\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max}, \widehat{v_t}) \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}} + \epsilon \big) \\ &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned}$$

For further details regarding the algorithm we refer to Adam: A Method for Stochastic Optimization.

Parameters:

• params (iterable) – iterable of parameters to optimize or dicts defining parameter groups

• lr (float, optional) – learning rate (default: 1e-3)

• betas (Tuple[float, float], optional) – coefficients used for computing running averages of gradient and its square (default: (0.9, 0.999))

• eps (float, optional) – term added to the denominator to improve numerical stability (default: 1e-8)

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

• amsgrad (bool, optional) – whether to use the AMSGrad variant of this algorithm from the paper On the Convergence of Adam and Beyond (default: False)

• foreach (bool, optional) – whether foreach implementation of optimizer is used. If unspecified by the user (so foreach is None), we will try to use foreach over the for-loop implementation on CUDA, since it is usually significantly more performant. (default: None)

• maximize (bool, optional) – maximize the params based on the objective, instead of minimizing (default: False)

• capturable (bool, optional) – whether this instance is safe to capture in a CUDA graph. Passing True can impair ungraphed performance, so if you don’t intend to graph capture this instance, leave it False (default: False)

• differentiable (bool, optional) – whether autograd should occur through the optimizer step in training. Otherwise, the step() function runs in a torch.no_grad() context. Setting to True can impair performance, so leave it False if you don’t intend to run autograd through this instance (default: False)

• fused (bool, optional) – whether the fused implementation (CUDA only) is used. Currently, torch.float64, torch.float32, torch.float16, and torch.bfloat16 are supported. (default: None)

Note

The foreach and fused implementations are typically faster than the for-loop, single-tensor implementation. Thus, if the user has not specified BOTH flags (i.e., when foreach = fused = None), we will attempt defaulting to the foreach implementation when the tensors are all on CUDA. For example, if the user specifies True for fused but nothing for foreach, we will run the fused implementation. If the user specifies False for foreach but nothing for fused (or False for fused but nothing for foreach), we will run the for-loop implementation. If the user specifies True for both foreach and fused, we will prioritize fused over foreach, as it is typically faster. We attempt to use the fastest, so the hierarchy goes fused -> foreach -> for-loop. HOWEVER, since the fused implementation is relatively new, we want to give it sufficient bake-in time, so we default to foreach and NOT fused when the user has not specified either flag.

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 calling handle.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 calling handle.remove()

Return type:

torch.utils.hooks.RemoveableHandle

state_dict()

Returns the state of the optimizer as a dict.

It contains two entries:

• state - a dict holding current optimization state. Its content

  differs between optimizer classes.

• param_groups - a list containing all parameter groups where each

  parameter group is a dict

zero_grad(set_to_none=True)

Resets the gradients of all optimized torch.Tensor s.

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).