""" PyTorch MADGRAD optimizer
MADGRAD: https://arxiv.org/abs/2101.11075
Code from: https://github.com/facebookresearch/madgrad
"""
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
import math
from typing import TYPE_CHECKING, Any, Callable, Optional
import torch
import torch.optim
if TYPE_CHECKING:
from torch.optim.optimizer import _params_t
else:
_params_t = Any
[docs]class MADGRAD(torch.optim.Optimizer):
"""
MADGRAD_: A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic
Optimization.
.. _MADGRAD: https://arxiv.org/abs/2101.11075
MADGRAD is a general purpose optimizer that can be used in place of SGD or
Adam may converge faster and generalize better. Currently GPU-only.
Typically, the same learning rate schedule that is used for SGD or Adam may
be used. The overall learning rate is not comparable to either method and
should be determined by a hyper-parameter sweep.
MADGRAD requires less weight decay than other methods, often as little as
zero. Momentum values used for SGD or Adam's beta1 should work here also.
On sparse problems both weight_decay and momentum should be set to 0.
Arguments:
params (iterable):
Iterable of parameters to optimize or dicts defining parameter groups.
lr (float):
Learning rate (default: 1e-2).
momentum (float):
Momentum value in the range [0,1) (default: 0.9).
weight_decay (float):
Weight decay, i.e. a L2 penalty (default: 0).
eps (float):
Term added to the denominator outside of the root operation to improve numerical stability. (default: 1e-6).
"""
def __init__(
self,
params: _params_t,
lr: float = 1e-2,
momentum: float = 0.9,
weight_decay: float = 0,
eps: float = 1e-6,
decoupled_decay: bool = False,
):
if momentum < 0 or momentum >= 1:
raise ValueError(f"Momentum {momentum} must be in the range [0,1]")
if lr <= 0:
raise ValueError(f"Learning rate {lr} must be positive")
if weight_decay < 0:
raise ValueError(f"Weight decay {weight_decay} must be non-negative")
if eps < 0:
raise ValueError(f"Eps must be non-negative")
defaults = dict(
lr=lr, eps=eps, momentum=momentum, weight_decay=weight_decay, decoupled_decay=decoupled_decay)
super().__init__(params, defaults)
@property
def supports_memory_efficient_fp16(self) -> bool:
return False
@property
def supports_flat_params(self) -> bool:
return True
[docs] @torch.no_grad()
def step(self, closure: Optional[Callable[[], float]] = None) -> Optional[float]:
"""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:
eps = group['eps']
lr = group['lr'] + eps
weight_decay = group['weight_decay']
momentum = group['momentum']
ck = 1 - momentum
for p in group["params"]:
if p.grad is None:
continue
grad = p.grad
if momentum != 0.0 and grad.is_sparse:
raise RuntimeError("momentum != 0 is not compatible with sparse gradients")
state = self.state[p]
if len(state) == 0:
state['step'] = 0
state['grad_sum_sq'] = torch.zeros_like(p)
state['s'] = torch.zeros_like(p)
if momentum != 0:
state['x0'] = torch.clone(p).detach()
state['step'] += 1
grad_sum_sq = state['grad_sum_sq']
s = state['s']
lamb = lr * math.sqrt(state['step'])
# Apply weight decay
if weight_decay != 0:
if group['decoupled_decay']:
p.mul_(1.0 - group['lr'] * weight_decay)
else:
if grad.is_sparse:
raise RuntimeError("weight_decay option is not compatible with sparse gradients")
grad.add_(p, alpha=weight_decay)
if grad.is_sparse:
grad = grad.coalesce()
grad_val = grad._values()
p_masked = p.sparse_mask(grad)
grad_sum_sq_masked = grad_sum_sq.sparse_mask(grad)
s_masked = s.sparse_mask(grad)
# Compute x_0 from other known quantities
rms_masked_vals = grad_sum_sq_masked._values().pow(1 / 3).add_(eps)
x0_masked_vals = p_masked._values().addcdiv(s_masked._values(), rms_masked_vals, value=1)
# Dense + sparse op
grad_sq = grad * grad
grad_sum_sq.add_(grad_sq, alpha=lamb)
grad_sum_sq_masked.add_(grad_sq, alpha=lamb)
rms_masked_vals = grad_sum_sq_masked._values().pow_(1 / 3).add_(eps)
s.add_(grad, alpha=lamb)
s_masked._values().add_(grad_val, alpha=lamb)
# update masked copy of p
p_kp1_masked_vals = x0_masked_vals.addcdiv(s_masked._values(), rms_masked_vals, value=-1)
# Copy updated masked p to dense p using an add operation
p_masked._values().add_(p_kp1_masked_vals, alpha=-1)
p.add_(p_masked, alpha=-1)
else:
if momentum == 0:
# Compute x_0 from other known quantities
rms = grad_sum_sq.pow(1 / 3).add_(eps)
x0 = p.addcdiv(s, rms, value=1)
else:
x0 = state['x0']
# Accumulate second moments
grad_sum_sq.addcmul_(grad, grad, value=lamb)
rms = grad_sum_sq.pow(1 / 3).add_(eps)
# Update s
s.add_(grad, alpha=lamb)
# Step
if momentum == 0:
p.copy_(x0.addcdiv(s, rms, value=-1))
else:
z = x0.addcdiv(s, rms, value=-1)
# p is a moving average of z
p.mul_(1 - ck).add_(z, alpha=ck)
return loss