# Copyright (C) 2024, François-Guillaume Fernandez.
# This program is licensed under the Apache License 2.0.
# See LICENSE or go to <https://www.apache.org/licenses/LICENSE-2.0> for full license details.
import math
from typing import Callable, Iterable, List, Optional, Tuple
import torch
from torch import Tensor
from torch.optim import Optimizer # type: ignore[attr-defined]
__all__ = ["AdEMAMix", "ademamix"]
[docs]
class AdEMAMix(Optimizer):
r"""Implements the AdEMAMix optimizer from `"The AdEMAMix Optimizer: Better, Faster, Older" <https://arxiv.org/pdf/2409.03137>`_.
The estimation of momentums is described as follows, :math:`\forall t \geq 1`:
.. math::
m_{1,t} \leftarrow \beta_1 m_{1, t-1} + (1 - \beta_1) g_t \\
m_{2,t} \leftarrow \beta_3 m_{2, t-1} + (1 - \beta_3) g_t \\
s_t \leftarrow \beta_2 s_{t-1} + (1 - \beta_2) (g_t - m_t)^2 + \epsilon
where :math:`g_t` is the gradient of :math:`\theta_t`,
:math:`\beta_1, \beta_2, \beta_3 \in [0, 1]^3` are the exponential average smoothing coefficients,
:math:`m_{1,0} = 0,\ m_{2,0} = 0,\ s_0 = 0`, :math:`\epsilon > 0`.
Then we correct their biases using:
.. math::
\hat{m_{1,t}} \leftarrow \frac{m_{1,t}}{1 - \beta_1^t} \\
\hat{s_t} \leftarrow \frac{s_t}{1 - \beta_2^t}
And finally the update step is performed using the following rule:
.. math::
\theta_t \leftarrow \theta_{t-1} - \eta \frac{\hat{m_{1,t}} + \alpha m_{2,t}}{\sqrt{\hat{s_t}} + \epsilon}
where :math:`\theta_t` is the parameter value at step :math:`t` (:math:`\theta_0` being the initialization value),
:math:`\eta` is the learning rate, :math:`\alpha > 0` :math:`\epsilon > 0`.
Args:
params (iterable): iterable of parameters to optimize or dicts defining parameter groups
lr (float, optional): learning rate
betas (Tuple[float, float, float], optional): coefficients used for running averages (default: (0.9, 0.999, 0.9999))
alpha (float, optional): the exponential decay rate of the second moment estimates (default: 5.0)
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)
amsgrad (bool, optional): whether to use the AMSGrad variant (default: False)
"""
def __init__(
self,
params: Iterable[torch.nn.Parameter],
lr: float = 1e-3,
betas: Tuple[float, float, float] = (0.9, 0.999, 0.9999),
alpha: float = 5.0,
eps: float = 1e-8,
weight_decay: float = 0.0,
) -> None:
if lr < 0.0:
raise ValueError(f"Invalid learning rate: {lr}")
if eps < 0.0:
raise ValueError(f"Invalid epsilon value: {eps}")
for idx, beta in enumerate(betas):
if not 0.0 <= beta < 1.0:
raise ValueError(f"Invalid beta parameter at index {idx}: {beta}")
defaults = {"lr": lr, "betas": betas, "alpha": alpha, "eps": eps, "weight_decay": weight_decay}
super().__init__(params, defaults)
@torch.no_grad()
def step(self, closure: Optional[Callable[[], float]] = None) -> Optional[float]: # type: ignore[override]
"""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:
params_with_grad = []
grads = []
exp_avgs = []
exp_avgs_slow = []
exp_avg_sqs = []
state_steps = []
for p in group["params"]:
if p.grad is not None:
params_with_grad.append(p)
if p.grad.is_sparse:
raise RuntimeError(f"{self.__class__.__name__} does not support sparse gradients")
grads.append(p.grad)
state = self.state[p]
# Lazy state initialization
if len(state) == 0:
state["step"] = 0
# Exponential moving average of gradient values
state["exp_avg"] = torch.zeros_like(p, memory_format=torch.preserve_format)
state["exp_avg_slow"] = torch.zeros_like(p, memory_format=torch.preserve_format)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(p, memory_format=torch.preserve_format)
exp_avgs.append(state["exp_avg"])
exp_avgs_slow.append(state["exp_avg_slow"])
exp_avg_sqs.append(state["exp_avg_sq"])
# update the steps for each param group update
state["step"] += 1
# record the step after step update
state_steps.append(state["step"])
beta1, beta2, beta3 = group["betas"]
ademamix(
params_with_grad,
grads,
exp_avgs,
exp_avgs_slow,
exp_avg_sqs,
state_steps,
beta1,
beta2,
beta3,
group["alpha"],
group["lr"],
group["weight_decay"],
group["eps"],
)
return loss
def ademamix(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avgs_slow: List[Tensor],
exp_avg_sqs: List[Tensor],
state_steps: List[int],
beta1: float,
beta2: float,
beta3: float,
alpha: float,
lr: float,
weight_decay: float,
eps: float,
) -> None:
r"""Functional API that performs AdaBelief algorithm computation.
See :class:`~holocron.optim.AdaBelief` for details.
"""
for i, param in enumerate(params):
grad = grads[i]
m1 = exp_avgs[i]
m2 = exp_avgs_slow[i]
nu = exp_avg_sqs[i]
step = state_steps[i]
bias_correction1 = 1 - beta1**step
bias_correction2 = 1 - beta2**step
if weight_decay != 0:
grad = grad.add(param, alpha=weight_decay)
# Decay the first and second moment running average coefficient
m1.mul_(beta1).add_(grad, alpha=1 - beta1)
nu.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
m2.mul_(beta3).add_(grad, alpha=1 - beta3)
denom = (nu.sqrt() / math.sqrt(bias_correction2)).add_(eps)
param.addcdiv_(m1 / bias_correction1 + alpha * m2, denom, value=-lr)