o <&iD@sddlZddlmZmZddlZddlmZddlmZmZm Z m Z m Z m Z m Z mZmZddgZGdddeZd d e d e d e_  d!deedeedeedeedeededeedededededededefddZdeedeedeedeedeededededededededefddZdeedeedeedeedeededededededededefdd ZdS)"N)ListOptional)Tensor) Optimizer_default_to_fused_or_foreach_differentiable_doc_dispatch_sqrt _foreach_doc _get_value_stack_if_compiling_use_grad_for_differentiable _view_as_realRAdamradamcsdeZdZ     ddddded eed effd d Zfd dZddZedddZ Z S)rMbP?g?g+?:0yE>rFN)foreachdifferentiabledecoupled_weight_decayrrc sd|ks td|d|kstd|d|dkr"dks,ntd|dd|dkr8dksBntd|dd|ksMtd |t|||||||d } t|| dS) NzInvalid learning rate: zInvalid epsilon value: r?z#Invalid beta parameter at index 0: rz#Invalid beta parameter at index 1: zInvalid weight_decay value: )lrbetaseps weight_decayrrr) ValueErrordictsuper__init__) selfparamsrrrrrrrdefaults __class__r?r@rArErFrBr&r&r'r(cs<   z RAdam.step)rrrrFN) __name__ __module__ __qualname__boolrr r*rDr r( __classcell__r&r&r$r'rs(    !aImplements RAdam algorithm. .. math:: \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)}, \textit{decoupled\_weight\_decay} \\ &\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{6mm} \theta_t \leftarrow \theta_{t-1} \\ &\hspace{6mm} \textbf{if} \: \lambda \neq 0 \\ &\hspace{12mm}\textbf{if} \: \textit{decoupled\_weight\_decay} \\ &\hspace{18mm} \theta_t \leftarrow \theta_{t} - \gamma \lambda \theta_{t} \\ &\hspace{12mm}\textbf{else} \\ &\hspace{18mm} g_t \leftarrow g_t + \lambda \theta_{t} \\ &\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 - \gamma \widehat{m_t} r_t l_t \\ &\hspace{6mm}\textbf{else} \\ &\hspace{12mm}\theta_t \leftarrow \theta_t - \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 provides an option to use either the original weight_decay implementation as in Adam (where the weight_decay is applied to the gradient) or the one from AdamW (where weight_decay is applied to the weight) through the decoupled_weight_decay option. When decoupled_weight_decay is set to False (default), it uses the original Adam style weight decay, otherwise, it uses the AdamW style which corresponds more closely to the `author's implementation`_ in the RAdam paper. Further information about decoupled weight decay can be found in `Decoupled Weight Decay Regularization`_. a Args: 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) decoupled_weight_decay (bool, optional): whether to use decoupled weight decay as in AdamW to obtain RAdamW (default: False) z a .. _On the variance of the adaptive learning rate and beyond: https://arxiv.org/abs/1908.03265 .. _author's implementation: https://github.com/LiyuanLucasLiu/RAdam .. _Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 Fr"r>r?r@rArrrrBrErFrrrc Cstdd|Ds td|durt||dd\}}|r%tjr%td|r/tjs/t}nt}||||||| | | | | |||d dS) zpFunctional API that performs RAdam algorithm computation. 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