import torch from torch.optim import Optimizer class Nadam(Optimizer): """Implements Nadam algorithm (a variant of Adam based on Nesterov momentum). It has been proposed in `Incorporating Nesterov Momentum into Adam`__. Arguments: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 2e-3) betas (Tuple[float, float], optional): coefficients used for computing running averages of gradient and its square 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) schedule_decay (float, optional): momentum schedule decay (default: 4e-3) __ http://cs229.stanford.edu/proj2015/054_report.pdf __ http://www.cs.toronto.edu/~fritz/absps/momentum.pdf Originally taken from: https://github.com/pytorch/pytorch/pull/1408 NOTE: Has potential issues but does work well on some problems. """ def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, schedule_decay=4e-3): defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, schedule_decay=schedule_decay) super(Nadam, self).__init__(params, defaults) 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 in self.param_groups: for p in group['params']: if p.grad is None: continue grad = p.grad.data state = self.state[p] # State initialization if len(state) == 0: state['step'] = 0 state['m_schedule'] = 1. state['exp_avg'] = grad.new().resize_as_(grad).zero_() state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_() # Warming momentum schedule m_schedule = state['m_schedule'] schedule_decay = group['schedule_decay'] exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq'] beta1, beta2 = group['betas'] eps = group['eps'] state['step'] += 1 t = state['step'] if group['weight_decay'] != 0: grad = grad.add(group['weight_decay'], p.data) momentum_cache_t = beta1 * \ (1. - 0.5 * (0.96 ** (t * schedule_decay))) momentum_cache_t_1 = beta1 * \ (1. - 0.5 * (0.96 ** ((t + 1) * schedule_decay))) m_schedule_new = m_schedule * momentum_cache_t m_schedule_next = m_schedule * momentum_cache_t * momentum_cache_t_1 state['m_schedule'] = m_schedule_new # 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) exp_avg_sq_prime = exp_avg_sq / (1. - beta2 ** t) denom = exp_avg_sq_prime.sqrt_().add_(eps) p.data.addcdiv_(-group['lr'] * (1. - momentum_cache_t) / (1. - m_schedule_new), grad, denom) p.data.addcdiv_(-group['lr'] * momentum_cache_t_1 / (1. - m_schedule_next), exp_avg, denom) return loss