#
# Cerebras implementation of NAdam optimizer. Adapted from the `torch.optim.NAdam` implementation.
#
# Copyright 2016-2023 Cerebras Systems
# SPDX-License-Identifier: BSD-3-Clause
#
from typing import Iterable, Tuple
import torch
import cerebras.pytorch as cstorch
from .optimizer import Optimizer
[docs]class NAdam(Optimizer):
r"""Implements NAdam algorithm to execute within the constraints
of the Cerebras WSE, including pre-initializing optimizer state.
Args:
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 (default: (0.9, 0.999))
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)
momentum_decay (float, optional): momentum momentum_decay (default: 4e-3)
foreach (bool, optional): whether foreach implementation of optimizer
is used (default: None)
For further details regarding the algorithm refer to
Incorporating Nesterov Momentum into Adam:
https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
"""
[docs] def __init__(
self,
params: Iterable[torch.nn.Parameter],
lr: float = 2e-3,
betas: Tuple[float, float] = (0.9, 0.999),
eps: float = 1e-8,
weight_decay: float = 0,
momentum_decay: float = 4e-3,
):
if lr < 0.0:
raise ValueError(f"Invalid learning rate: {lr}")
if eps < 0.0:
raise ValueError(f"Invalid epsilon value: {eps}")
if not 0.0 <= betas[0] < 1.0:
raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
if not 0.0 <= betas[1] < 1.0:
raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
if weight_decay < 0.0:
raise ValueError(f"Invalid weight_decay value: {weight_decay}")
if momentum_decay < 0.0:
raise ValueError(f"Invalid momentum_decay value: {momentum_decay}")
defaults = dict(
lr=lr,
betas=betas,
eps=eps,
weight_decay=weight_decay,
momentum_decay=momentum_decay,
)
super().__init__(params, defaults, enable_global_step=True)
[docs] def preinitialize(self):
"""Allocates tensors for the optimizer state to allow direct compilation
of the model before the first step.
"""
for group in self.param_groups:
for p in group['params']:
self.state[p]["mu_product"] = torch.tensor(1.0).to(p.device)
self.state[p]["exp_avg"] = cstorch.zeros_like(p)
self.state[p]["exp_avg_sq"] = cstorch.zeros_like(p)
@torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Args:
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:
weight_decay = group["weight_decay"]
beta1, beta2 = group["betas"]
if not isinstance(beta2, torch.Tensor):
beta2 = torch.tensor(beta2)
momentum_decay = group["momentum_decay"]
eps = group["eps"]
lr = group["lr"]
for p in group['params']:
if p.grad is not None:
if p.grad.is_sparse:
raise RuntimeError(
'NAdam does not support sparse gradients'
)
state = self.state[p]
exp_avg = state["exp_avg"]
exp_avg_sq = state["exp_avg_sq"]
mu_product = state["mu_product"]
global_step = self.increment_global_step(p)
beta2t = torch.pow(beta2.to(p.device), global_step)
bias_correction2 = 1 - beta2t
grad = p.grad
if weight_decay > 0.0:
grad.add_(p, alpha=weight_decay)
# calculate the momentum cache \mu^{t} and \mu^{t+1}
point_nine_six = torch.tensor(0.96).to(p.device)
mu_pow = torch.pow(
point_nine_six, (global_step * momentum_decay)
)
mu = beta1 * (1.0 - 0.5 * (mu_pow))
mu_next_pow = torch.pow(
point_nine_six,
((global_step + 1) * momentum_decay),
)
mu_next = beta1 * (1.0 - 0.5 * (mu_next_pow))
# update the mu_product
mu_product *= mu
mu_product_next = mu_product * mu * mu_next
# decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(grad, alpha=1.0 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(
grad, grad, value=1.0 - beta2
)
# denom of the update step
denom = exp_avg_sq.div(bias_correction2).sqrt().add_(eps)
# num of the update step without lr
momentum_update = (mu_next * exp_avg) / (
1.0 - mu_product_next
)
grad_update = (grad * (1.0 - mu)) / (1.0 - mu_product)
update = momentum_update + grad_update
# multiply with lr
update *= -lr
# update params
p.addcdiv_(update, denom)
return loss