pytorch/torch/optim/rmsprop.py

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


class RMSprop(Optimizer):
    r"""Implements RMSprop algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \alpha \text{ (alpha)},\: \gamma \text{ (lr)},
                \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}                   \\
            &\hspace{13mm}   \lambda \text{ (weight decay)},\: \mu \text{ (momentum)},\: centered\\
            &\textbf{initialize} : v_0 \leftarrow 0 \text{ (square average)}, \:
                \textbf{b}_0 \leftarrow 0 \text{ (buffer)}, \: g^{ave}_0 \leftarrow 0     \\[-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}v_t           \leftarrow   \alpha v_{t-1} + (1 - \alpha) g^2_t
                \hspace{8mm}                                                                     \\
            &\hspace{5mm} \tilde{v_t} \leftarrow v_t                                             \\
            &\hspace{5mm}if \: centered                                                          \\
            &\hspace{10mm} g^{ave}_t \leftarrow g^{ave}_{t-1} \alpha + (1-\alpha) g_t            \\
            &\hspace{10mm} \tilde{v_t} \leftarrow \tilde{v_t} -  \big(g^{ave}_{t} \big)^2        \\
            &\hspace{5mm}if \: \mu > 0                                                           \\
            &\hspace{10mm} \textbf{b}_t\leftarrow \mu \textbf{b}_{t-1} +
                g_t/ \big(\sqrt{\tilde{v_t}} +  \epsilon \big)                                   \\
            &\hspace{10mm} \theta_t \leftarrow \theta_{t-1} - \gamma \textbf{b}_t                \\
            &\hspace{5mm} else                                                                   \\
            &\hspace{10mm}\theta_t      \leftarrow   \theta_{t-1} -
                \gamma  g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big)  \hspace{3mm}              \\
            &\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
    `lecture notes <https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf>`_ by G. Hinton.
    and centered version `Generating Sequences
    With Recurrent Neural Networks <https://arxiv.org/pdf/1308.0850v5.pdf>`_.
    The implementation here takes the square root of the gradient average before
    adding epsilon (note that TensorFlow interchanges these two operations). The effective
    learning rate is thus :math:`\gamma/(\sqrt{v} + \epsilon)` where :math:`\gamma`
    is the scheduled learning rate and :math:`v` is the weighted moving average
    of the squared gradient.

    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-2)
        momentum (float, optional): momentum factor (default: 0)
        alpha (float, optional): smoothing constant (default: 0.99)
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        centered (bool, optional) : if ``True``, compute the centered RMSProp,
            the gradient is normalized by an estimation of its variance
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)

    """

    def __init__(self, params, lr=1e-2, alpha=0.99, eps=1e-8, weight_decay=0, momentum=0, centered=False):
        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 <= momentum:
            raise ValueError("Invalid momentum value: {}".format(momentum))
        if not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
        if not 0.0 <= alpha:
            raise ValueError("Invalid alpha value: {}".format(alpha))

        defaults = dict(lr=lr, momentum=momentum, alpha=alpha, eps=eps, centered=centered, weight_decay=weight_decay)
        super(RMSprop, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(RMSprop, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault('momentum', 0)
            group.setdefault('centered', False)

    @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 = []
            square_avgs = []
            grad_avgs = []
            momentum_buffer_list = []

            for p in group['params']:
                if p.grad is None:
                    continue
                params_with_grad.append(p)

                if p.grad.is_sparse:
                    raise RuntimeError('RMSprop does not support sparse gradients')
                grads.append(p.grad)

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    state['square_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    if group['momentum'] > 0:
                        state['momentum_buffer'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    if group['centered']:
                        state['grad_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                square_avgs.append(state['square_avg'])

                if group['momentum'] > 0:
                    momentum_buffer_list.append(state['momentum_buffer'])
                if group['centered']:
                    grad_avgs.append(state['grad_avg'])

                state['step'] += 1


            F.rmsprop(params_with_grad,
                      grads,
                      square_avgs,
                      grad_avgs,
                      momentum_buffer_list,
                      lr=group['lr'],
                      alpha=group['alpha'],
                      eps=group['eps'],
                      weight_decay=group['weight_decay'],
                      momentum=group['momentum'],
                      centered=group['centered'])

        return loss