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import math
import torch
from torch.optim.optimizer 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):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
defaults = dict(
lr=lr,
betas=betas,
eps=eps,
weight_decay=weight_decay,
schedule_decay=schedule_decay,
)
super(Nadam, self).__init__(params, defaults)
@torch.no_grad()
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:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad = p.grad
state = self.state[p]
# State initialization
if len(state) == 0:
state['step'] = 0
state['m_schedule'] = 1.
state['exp_avg'] = torch.zeros_like(p)
state['exp_avg_sq'] = torch.zeros_like(p)
# 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']
bias_correction2 = 1 - beta2 ** t
if group['weight_decay'] != 0:
grad = grad.add(p, alpha=group['weight_decay'])
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_(grad, alpha=1. - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1. - beta2)
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps)
p.addcdiv_(grad, denom, value=-group['lr'] * (1. - momentum_cache_t) / (1. - m_schedule_new))
p.addcdiv_(exp_avg, denom, value=-group['lr'] * momentum_cache_t_1 / (1. - m_schedule_next))
return loss
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