import torch from torch import Tensor from .optimizer import Optimizer from typing import List, Optional 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 `_ by G. Hinton. and centered version `Generating Sequences With Recurrent Neural Networks `_. 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) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) """ def __init__(self, params, lr=1e-2, alpha=0.99, eps=1e-8, weight_decay=0, momentum=0, centered=False, foreach: Optional[bool] = None): 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, foreach=foreach) super(RMSprop, self).__init__(params, defaults) def __setstate__(self, state): super().__setstate__(state) for group in self.param_groups: group.setdefault('momentum', 0) group.setdefault('centered', False) group.setdefault('foreach', None) @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 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'], foreach=group['foreach']) return loss def rmsprop(params: List[Tensor], grads: List[Tensor], square_avgs: List[Tensor], grad_avgs: List[Tensor], momentum_buffer_list: List[Tensor], # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627 # setting this as kwarg for now as functional API is compiled by torch/distributed/optim foreach: bool = None, *, lr: float, alpha: float, eps: float, weight_decay: float, momentum: float, centered: bool): r"""Functional API that performs rmsprop algorithm computation. See :class:`~torch.optim.RMSProp` for details. """ if foreach is None: # Placeholder for more complex foreach logic to be added when value is not set foreach = False if foreach and torch.jit.is_scripting(): raise RuntimeError('torch.jit.script not supported with foreach optimizers') if foreach and not torch.jit.is_scripting(): func = _multi_tensor_rmsprop else: func = _single_tensor_rmsprop func(params, grads, square_avgs, grad_avgs, momentum_buffer_list, lr=lr, alpha=alpha, eps=eps, weight_decay=weight_decay, momentum=momentum, centered=centered) def _single_tensor_rmsprop(params: List[Tensor], grads: List[Tensor], square_avgs: List[Tensor], grad_avgs: List[Tensor], momentum_buffer_list: List[Tensor], *, lr: float, alpha: float, eps: float, weight_decay: float, momentum: float, centered: bool): for i, param in enumerate(params): grad = grads[i] square_avg = square_avgs[i] if weight_decay != 0: grad = grad.add(param, alpha=weight_decay) square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha) if centered: grad_avg = grad_avgs[i] grad_avg.mul_(alpha).add_(grad, alpha=1 - alpha) avg = square_avg.addcmul(grad_avg, grad_avg, value=-1).sqrt_().add_(eps) else: avg = square_avg.sqrt().add_(eps) if momentum > 0: buf = momentum_buffer_list[i] buf.mul_(momentum).addcdiv_(grad, avg) param.add_(buf, alpha=-lr) else: param.addcdiv_(grad, avg, value=-lr) def _multi_tensor_rmsprop(params: List[Tensor], grads: List[Tensor], square_avgs: List[Tensor], grad_avgs: List[Tensor], momentum_buffer_list: List[Tensor], *, lr: float, alpha: float, eps: float, weight_decay: float, momentum: float, centered: bool): if len(params) == 0: return if weight_decay != 0: torch._foreach_add_(grads, params, alpha=weight_decay) torch._foreach_mul_(square_avgs, alpha) torch._foreach_addcmul_(square_avgs, grads, grads, value=1 - alpha) if centered: torch._foreach_mul_(grad_avgs, alpha) torch._foreach_add_(grad_avgs, grads, alpha=1 - alpha) avg = torch._foreach_addcmul(square_avgs, grad_avgs, grad_avgs, value=-1) torch._foreach_sqrt_(avg) torch._foreach_add_(avg, eps) else: avg = torch._foreach_sqrt(square_avgs) torch._foreach_add_(avg, eps) if momentum > 0: torch._foreach_mul_(momentum_buffer_list, momentum) torch._foreach_addcdiv_(momentum_buffer_list, grads, avg) torch._foreach_add_(params, momentum_buffer_list, alpha=-lr) else: torch._foreach_addcdiv_(params, grads, avg, value=-lr)