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import math
import torch
from ..optimizer import Optimizer
class ASGD(Optimizer):
"""Implements Averaged Stochastic Gradient Descent.
It has been proposed in `Acceleration of stochastic approximation by
averaging`_.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-2)
lambd (float, optional): decay term (default: 1e-4)
alpha (float, optional): power for eta update (default: 0.75)
t0 (float, optional): point at which to start averaging (default: 1e6)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
.. _Acceleration of stochastic approximation by averaging:
https://dl.acm.org/citation.cfm?id=131098
"""
def __init__(self, params, lr=1e-2, lambd=1e-4, alpha=0.75, t0=1e6, weight_decay=0):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <= weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, lambd=lambd, alpha=alpha, t0=t0,
weight_decay=weight_decay)
super(ASGD, 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()
grads = []
params_with_grad = []
states = []
for group in self.param_groups:
for p in group['params']:
if p.grad is not None:
if p.grad.is_sparse:
raise RuntimeError('ASGD does not support sparse gradients')
grads.append(p.grad)
params_with_grad.append(p)
state = self.state[p]
# State initialization
if len(state) == 0:
state['step'] = 0
state['eta'] = group['lr']
state['mu'] = 1
state['ax'] = torch.zeros_like(p, memory_format=torch.preserve_format)
state['step'] += 1
states.append(state)
if group['weight_decay'] != 0:
torch._foreach_add_(grads, params_with_grad, alpha=group['weight_decay'])
# decay term
torch._foreach_mul_(params_with_grad, 1 - group['lambd'] * state['eta'])
# update parameter
torch._foreach_add_(params_with_grad, grads, alpha=-state['eta'])
# averaging
for i in range(len(states)):
if states[i]['mu'] != 1:
states[i]['ax'].add_(params_with_grad[i].sub(states[i]['ax']).mul(states[i]['mu']))
else:
states[i]['ax'].copy_(params_with_grad[i])
# update eta and mu
for state in states:
state['eta'] = (group['lr'] /
math.pow((1 + group['lambd'] * group['lr'] * state['step']), group['alpha']))
state['mu'] = 1 / max(1, state['step'] - group['t0'])
return loss
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