Source code for torch.optim.nadam

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


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:
        https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
    """

    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)

    @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