import math import torch from torch.optim import Optimizer class AdaBound(Optimizer): """Implements AdaBound algorithm. It has been proposed in `Adaptive Gradient Methods with Dynamic Bound of Learning Rate`_. Arguments: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): Adam learning rate (default: 1e-3) betas (Tuple[float, float], optional): coefficients used for computing running averages of gradient and its square (default: (0.9, 0.999)) final_lr (float, optional): final (SGD) learning rate (default: 0.1) gamma (float, optional): convergence speed of the bound functions (default: 1e-3) 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) amsbound (boolean, optional): whether to use the AMSBound variant of this algorithm .. Adaptive Gradient Methods with Dynamic Bound of Learning Rate: https://openreview.net/forum?id=Bkg3g2R9FX """ def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), final_lr=0.1, gamma=1e-3, eps=1e-8, weight_decay=0, amsbound=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 <= 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 <= final_lr: raise ValueError("Invalid final learning rate: {}".format(final_lr)) if not 0.0 <= gamma < 1.0: raise ValueError("Invalid gamma parameter: {}".format(gamma)) defaults = dict(lr=lr, betas=betas, final_lr=final_lr, gamma=gamma, eps=eps, weight_decay=weight_decay, amsbound=amsbound) super(AdaBound, self).__init__(params, defaults) self.base_lrs = list(map(lambda group: group['lr'], self.param_groups)) def __setstate__(self, state): super(AdaBound, self).__setstate__(state) for group in self.param_groups: group.setdefault('amsbound', False) def step(self, closure=None): """Performs a single optimization step. Arguments: closure (callable, optional): A closure that reevaluates the model and returns the loss. """ loss = None if closure is not None: loss = closure() for group, base_lr in zip(self.param_groups, self.base_lrs): for p in group['params']: if p.grad is None: continue grad = p.grad.data if grad.is_sparse: raise RuntimeError( 'Adam does not support sparse gradients, please consider SparseAdam instead') amsbound = group['amsbound'] state = self.state[p] # State initialization if len(state) == 0: state['step'] = 0 # Exponential moving average of gradient values state['exp_avg'] = torch.zeros_like(p.data) # Exponential moving average of squared gradient values state['exp_avg_sq'] = torch.zeros_like(p.data) if amsbound: # Maintains max of all exp. moving avg. of sq. grad. values state['max_exp_avg_sq'] = torch.zeros_like(p.data) exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq'] if amsbound: max_exp_avg_sq = state['max_exp_avg_sq'] beta1, beta2 = group['betas'] state['step'] += 1 if group['weight_decay'] != 0: grad = grad.add(group['weight_decay'], p.data) # Decay the first and second moment running average coefficient exp_avg.mul_(beta1).add_(1 - beta1, grad) exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad) if amsbound: # Maintains the maximum of all 2nd moment running avg. till now torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq) # Use the max. for normalizing running avg. of gradient denom = max_exp_avg_sq.sqrt().add_(group['eps']) else: denom = exp_avg_sq.sqrt().add_(group['eps']) bias_correction1 = 1 - beta1 ** state['step'] bias_correction2 = 1 - beta2 ** state['step'] step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1 # Applies bounds on actual learning rate # lr_scheduler cannot affect final_lr, this is a workaround to apply lr decay final_lr = group['final_lr'] * group['lr'] / base_lr lower_bound = final_lr * (1 - 1 / (group['gamma'] * state['step'] + 1)) upper_bound = final_lr * (1 + 1 / (group['gamma'] * state['step'])) step_size = torch.full_like(denom, step_size) step_size.div_(denom).clamp_(lower_bound, upper_bound).mul_(exp_avg) p.data.add_(-step_size) return loss