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import torch
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from torch.optim import Optimizer
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class Nadam(Optimizer):
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"""Implements Nadam algorithm (a variant of Adam based on Nesterov momentum).
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It has been proposed in `Incorporating Nesterov Momentum into Adam`__.
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Arguments:
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params (iterable): iterable of parameters to optimize or dicts defining
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parameter groups
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lr (float, optional): learning rate (default: 2e-3)
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betas (Tuple[float, float], optional): coefficients used for computing
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running averages of gradient and its square
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eps (float, optional): term added to the denominator to improve
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numerical stability (default: 1e-8)
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weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
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schedule_decay (float, optional): momentum schedule decay (default: 4e-3)
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__ http://cs229.stanford.edu/proj2015/054_report.pdf
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__ http://www.cs.toronto.edu/~fritz/absps/momentum.pdf
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Originally taken from: https://github.com/pytorch/pytorch/pull/1408
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NOTE: Has potential issues but does work well on some problems.
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"""
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def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
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weight_decay=0, schedule_decay=4e-3):
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defaults = dict(lr=lr, betas=betas, eps=eps,
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weight_decay=weight_decay, schedule_decay=schedule_decay)
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super(Nadam, self).__init__(params, defaults)
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def step(self, closure=None):
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"""Performs a single optimization step.
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Arguments:
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closure (callable, optional): A closure that reevaluates the model
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and returns the loss.
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"""
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loss = None
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if closure is not None:
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loss = closure()
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for group in self.param_groups:
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for p in group['params']:
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if p.grad is None:
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continue
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grad = p.grad.data
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state = self.state[p]
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# State initialization
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if len(state) == 0:
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state['step'] = 0
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state['m_schedule'] = 1.
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state['exp_avg'] = grad.new().resize_as_(grad).zero_()
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state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()
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# Warming momentum schedule
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m_schedule = state['m_schedule']
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schedule_decay = group['schedule_decay']
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exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
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beta1, beta2 = group['betas']
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eps = group['eps']
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state['step'] += 1
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t = state['step']
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if group['weight_decay'] != 0:
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grad = grad.add(group['weight_decay'], p.data)
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momentum_cache_t = beta1 * \
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(1. - 0.5 * (0.96 ** (t * schedule_decay)))
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momentum_cache_t_1 = beta1 * \
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(1. - 0.5 * (0.96 ** ((t + 1) * schedule_decay)))
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m_schedule_new = m_schedule * momentum_cache_t
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m_schedule_next = m_schedule * momentum_cache_t * momentum_cache_t_1
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state['m_schedule'] = m_schedule_new
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# Decay the first and second moment running average coefficient
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exp_avg.mul_(beta1).add_(1. - beta1, grad)
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exp_avg_sq.mul_(beta2).addcmul_(1. - beta2, grad, grad)
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exp_avg_sq_prime = exp_avg_sq / (1. - beta2 ** t)
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denom = exp_avg_sq_prime.sqrt_().add_(eps)
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p.data.addcdiv_(-group['lr'] * (1. - momentum_cache_t) / (1. - m_schedule_new), grad, denom)
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p.data.addcdiv_(-group['lr'] * momentum_cache_t_1 / (1. - m_schedule_next), exp_avg, denom)
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return loss
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