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# RAdam¶

class torch.optim.RAdam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, *, foreach=None, differentiable=False)[source]

Implements RAdam 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)}, \: \lambda \text{ (weightdecay)}, \\ &\hspace{13mm} \epsilon \text{ (epsilon)} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, v_0 \leftarrow 0 \text{ ( second moment)}, \\ &\hspace{18mm} \rho_{\infty} \leftarrow 2/(1-\beta_2) -1 \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{6mm}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{6mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ &\hspace{6mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\ &\hspace{6mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\ &\hspace{6mm}\rho_t \leftarrow \rho_{\infty} - 2 t \beta^t_2 /\big(1-\beta_2^t \big) \\[0.1.ex] &\hspace{6mm}\textbf{if} \: \rho_t > 5 \\ &\hspace{12mm} l_t \leftarrow \frac{\sqrt{ (1-\beta^t_2) }}{ \sqrt{v_t} +\epsilon } \\ &\hspace{12mm} r_t \leftarrow \sqrt{\frac{(\rho_t-4)(\rho_t-2)\rho_{\infty}}{(\rho_{\infty}-4)(\rho_{\infty}-2) \rho_t}} \\ &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} r_t l_t \\ &\hspace{6mm}\textbf{else} \\ &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} \\ &\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 On the variance of the adaptive learning rate and beyond.

This implementation uses the same weight_decay implementation as Adam (were the weight_decay is applied to the gradient) and not the one from AdamW (were weight_decay is applied to the update). This is different from the author’s implementation.

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)

• 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)

• 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)

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)

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).

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