import torch from torch import Tensor from .optimizer import Optimizer from typing import List, Optional class Rprop(Optimizer): r"""Implements the resilient backpropagation algorithm. .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \theta_0 \in \mathbf{R}^d \text{ (params)},f(\theta) \text{ (objective)}, \\ &\hspace{13mm} \eta_{+/-} \text{ (etaplus, etaminus)}, \Gamma_{max/min} \text{ (step sizes)} \\ &\textbf{initialize} : g^0_{prev} \leftarrow 0, \: \eta_0 \leftarrow \text{lr (learning rate)} \\ &\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} \textbf{for} \text{ } i = 0, 1, \ldots, d-1 \: \mathbf{do} \\ &\hspace{10mm} \textbf{if} \: g^i_{prev} g^i_t > 0 \\ &\hspace{15mm} \eta^i_t \leftarrow \mathrm{min}(\eta^i_{t-1} \eta_{+}, \Gamma_{max}) \\ &\hspace{10mm} \textbf{else if} \: g^i_{prev} g^i_t < 0 \\ &\hspace{15mm} \eta^i_t \leftarrow \mathrm{max}(\eta^i_{t-1} \eta_{-}, \Gamma_{min}) \\ &\hspace{15mm} g^i_t \leftarrow 0 \\ &\hspace{10mm} \textbf{else} \: \\ &\hspace{15mm} \eta^i_t \leftarrow \eta^i_{t-1} \\ &\hspace{5mm}\theta_t \leftarrow \theta_{t-1}- \eta_t \mathrm{sign}(g_t) \\ &\hspace{5mm}g_{prev} \leftarrow g_t \\ &\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 the paper `A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm `_. Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 1e-2) etas (Tuple[float, float], optional): pair of (etaminus, etaplis), that are multiplicative increase and decrease factors (default: (0.5, 1.2)) step_sizes (Tuple[float, float], optional): a pair of minimal and maximal allowed step sizes (default: (1e-6, 50)) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) """ def __init__(self, params, lr=1e-2, etas=(0.5, 1.2), step_sizes=(1e-6, 50), foreach: Optional[bool] = None): if not 0.0 <= lr: raise ValueError("Invalid learning rate: {}".format(lr)) if not 0.0 < etas[0] < 1.0 < etas[1]: raise ValueError("Invalid eta values: {}, {}".format(etas[0], etas[1])) defaults = dict(lr=lr, etas=etas, step_sizes=step_sizes, foreach=foreach) super(Rprop, self).__init__(params, defaults) def __setstate__(self, state): super().__setstate__(state) for group in self.param_groups: 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 = [] grads = [] prevs = [] step_sizes = [] etaminus, etaplus = group['etas'] step_size_min, step_size_max = group['step_sizes'] foreach = group['foreach'] for p in group['params']: if p.grad is None: continue params.append(p) grad = p.grad if grad.is_sparse: raise RuntimeError('Rprop does not support sparse gradients') grads.append(grad) state = self.state[p] # State initialization if len(state) == 0: state['step'] = 0 state['prev'] = torch.zeros_like(p, memory_format=torch.preserve_format) state['step_size'] = grad.new().resize_as_(grad).fill_(group['lr']) prevs.append(state['prev']) step_sizes.append(state['step_size']) state['step'] += 1 rprop(params, grads, prevs, step_sizes, step_size_min=step_size_min, step_size_max=step_size_max, etaminus=etaminus, etaplus=etaplus, foreach=foreach) return loss def rprop(params: List[Tensor], grads: List[Tensor], prevs: List[Tensor], step_sizes: 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, *, step_size_min: float, step_size_max: float, etaminus: float, etaplus: float): r"""Functional API that performs rprop algorithm computation. See :class:`~torch.optim.Rprop` 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_rprop else: func = _single_tensor_rprop func(params, grads, prevs, step_sizes, step_size_min=step_size_min, step_size_max=step_size_max, etaminus=etaminus, etaplus=etaplus) def _single_tensor_rprop(params: List[Tensor], grads: List[Tensor], prevs: List[Tensor], step_sizes: List[Tensor], *, step_size_min: float, step_size_max: float, etaminus: float, etaplus: float): for i, param in enumerate(params): grad = grads[i] prev = prevs[i] step_size = step_sizes[i] sign = grad.mul(prev).sign() sign[sign.gt(0)] = etaplus sign[sign.lt(0)] = etaminus sign[sign.eq(0)] = 1 # update stepsizes with step size updates step_size.mul_(sign).clamp_(step_size_min, step_size_max) # for dir<0, dfdx=0 # for dir>=0 dfdx=dfdx grad = grad.clone(memory_format=torch.preserve_format) grad[sign.eq(etaminus)] = 0 # update parameters param.addcmul_(grad.sign(), step_size, value=-1) prev.copy_(grad) def _multi_tensor_rprop(params: List[Tensor], grads: List[Tensor], prevs: List[Tensor], step_sizes: List[Tensor], *, step_size_min: float, step_size_max: float, etaminus: float, etaplus: float): if len(params) == 0: return signs = torch._foreach_mul(grads, prevs) signs = [s.sign() for s in signs] for sign in signs: sign[sign.gt(0)] = etaplus sign[sign.lt(0)] = etaminus sign[sign.eq(0)] = 1 # update stepsizes with step size updates torch._foreach_mul_(step_sizes, signs) for step_size in step_sizes: step_size.clamp_(step_size_min, step_size_max) # for dir<0, dfdx=0 # for dir>=0 dfdx=dfdx for i in range(len(grads)): grads[i] = grads[i].clone(memory_format=torch.preserve_format) grads[i][signs[i].eq(etaminus)] = 0 # update parameters grad_signs = [grad.sign() for grad in grads] torch._foreach_addcmul_(params, grad_signs, step_sizes, value=-1) for i in range(len(prevs)): prevs[i].copy_(grads[i])