Source code for torch.optim.nadam

import torch
from . import _functional as F
from .optimizer import Optimizer

[docs]class NAdam(Optimizer): r"""Implements NAdam algorithm. .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)} \\ &\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, v_0 \leftarrow 0 \text{ ( second moment)} \\[-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}if \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{t \psi} \big) \\ &\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\ &\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 \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex] & \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i}) \\ &\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\ &\hspace{5mm}\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 `Incorporating Nesterov Momentum into Adam`_. Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 2e-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) momentum_decay (float, optional): momentum momentum_decay (default: 4e-3) .. _Incorporating Nesterov Momentum into Adam: """ def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, momentum_decay=4e-3): if not 0.0 <= lr: raise ValueError("Invalid learning rate: {}".format(lr)) if not 0.0 <= eps: raise ValueError("Invalid epsilon value: {}".format(eps)) if not 0.0 <= betas[0] < 1.0: raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0])) if not 0.0 <= betas[1] < 1.0: raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1])) if not 0.0 <= weight_decay: raise ValueError("Invalid weight_decay value: {}".format(weight_decay)) if not 0.0 <= momentum_decay: raise ValueError("Invalid momentum_decay value: {}".format(momentum_decay)) defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, momentum_decay=momentum_decay) super(NAdam, self).__init__(params, defaults)
[docs] @torch.no_grad() def step(self, closure=None): """Performs a single optimization step. Args: closure (callable, optional): A closure that reevaluates the model and returns the loss. """ loss = None if closure is not None: with torch.enable_grad(): loss = closure() for group in self.param_groups: params_with_grad = [] grads = [] exp_avgs = [] exp_avg_sqs = [] mu_products = [] state_steps = [] beta1, beta2 = group['betas'] for p in group['params']: if p.grad is not None: params_with_grad.append(p) if p.grad.is_sparse: raise RuntimeError('NAdam does not support sparse gradients') grads.append(p.grad) state = self.state[p] # Lazy state initialization if len(state) == 0: state['step'] = 0 state['mu_product'] = 1. # Exponential moving average of gradient values state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format) # Exponential moving average of squared gradient values state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format) exp_avgs.append(state['exp_avg']) exp_avg_sqs.append(state['exp_avg_sq']) mu_products.append(state['mu_product']) # update the steps for each param group update state['step'] += 1 # record the step after step update state_steps.append(state['step']) F.nadam(params_with_grad, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps, beta1=beta1, beta2=beta2, lr=group['lr'], weight_decay=group['weight_decay'], momentum_decay=group['momentum_decay'], eps=group['eps']) # update mu_product for p, mu_product in zip(params_with_grad, mu_products): state = self.state[p] state['mu_product'] = state['mu_product'] * beta1 * \ (1. - 0.5 * (0.96 ** (state['step'] * group['momentum_decay']))) return loss


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