| import torch |
| from torch import Tensor |
| from .optimizer import Optimizer, _use_grad_for_differentiable |
| from typing import List, Optional |
| |
| __all__ = ["RMSprop", "rmsprop"] |
| |
| |
| 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) |
| foreach (bool, optional): whether foreach implementation of optimizer |
| is used (default: None) |
| maximize (bool, optional): maximize the params based on the objective, instead of |
| minimizing (default: False) |
| |
| """ |
| |
| def __init__( |
| self, |
| params, |
| lr=1e-2, |
| alpha=0.99, |
| eps=1e-8, |
| weight_decay=0, |
| momentum=0, |
| centered=False, |
| foreach: Optional[bool] = None, |
| maximize: bool = False, |
| differentiable: bool = 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, |
| foreach=foreach, |
| maximize=maximize, |
| differentiable=differentiable, |
| ) |
| 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) |
| group.setdefault("maximize", False) |
| group.setdefault("differentiable", False) |
| |
| def _init_group(self, group, params_with_grad, grads, square_avgs, momentum_buffer_list, grad_avgs): |
| 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"]) |
| |
| if group["differentiable"] and isinstance(state["step"], Tensor): |
| raise RuntimeError("`step` can't be a tensor") |
| |
| state["step"] += 1 |
| |
| @_use_grad_for_differentiable |
| 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 = [] |
| |
| self._init_group(group, params_with_grad, grads, square_avgs, momentum_buffer_list, grad_avgs) |
| |
| 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"], |
| maximize=group["maximize"], |
| differentiable=group["differentiable"], |
| ) |
| |
| 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, |
| maximize: bool = False, |
| differentiable: bool = False, |
| *, |
| 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, |
| maximize=maximize, |
| differentiable=differentiable, |
| ) |
| |
| |
| 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, |
| maximize: bool, |
| differentiable: bool, |
| ): |
| |
| for i, param in enumerate(params): |
| grad = grads[i] |
| grad = grad if not maximize else -grad |
| square_avg = square_avgs[i] |
| |
| if weight_decay != 0: |
| grad = grad.add(param, alpha=weight_decay) |
| |
| is_complex_param = torch.is_complex(param) |
| if is_complex_param: |
| param = torch.view_as_real(param) |
| grad = torch.view_as_real(grad) |
| square_avg = torch.view_as_real(square_avg) |
| |
| square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha) |
| |
| if centered: |
| grad_avg = grad_avgs[i] |
| if is_complex_param: |
| grad_avg = torch.view_as_real(grad_avg) |
| grad_avg.mul_(alpha).add_(grad, alpha=1 - alpha) |
| avg = square_avg.addcmul(grad_avg, grad_avg, value=-1).sqrt_() |
| else: |
| avg = square_avg.sqrt() |
| |
| if differentiable: |
| avg = avg.add(eps) |
| else: |
| avg = avg.add_(eps) |
| |
| if momentum > 0: |
| buf = momentum_buffer_list[i] |
| if is_complex_param: |
| buf = torch.view_as_real(buf) |
| 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, |
| maximize: bool, |
| differentiable: bool, |
| ): |
| |
| if len(params) == 0: |
| return |
| |
| assert not differentiable, "_foreach ops don't support autograd" |
| |
| if maximize: |
| grads = torch._foreach_neg(grads) |
| |
| if weight_decay != 0: |
| torch._foreach_add_(grads, params, alpha=weight_decay) |
| |
| def _view_complex_as_real(tensor_list): |
| return [ |
| torch.view_as_real(t) if torch.is_complex(t) else t for t in tensor_list |
| ] |
| |
| grads = _view_complex_as_real(grads) |
| params = _view_complex_as_real(params) |
| square_avgs = _view_complex_as_real(square_avgs) |
| |
| torch._foreach_mul_(square_avgs, alpha) |
| torch._foreach_addcmul_(square_avgs, grads, grads, value=1 - alpha) |
| |
| if centered: |
| grad_avgs = _view_complex_as_real(grad_avgs) |
| 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: |
| momentum_buffer_list = _view_complex_as_real(momentum_buffer_list) |
| 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) |
