# Copyright (C) 2019-2024, 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.
from typing import Callable, Iterable, Optional, Tuple
import torch
from torch.optim.optimizer import Optimizer
__all__ = ["LAMB"]
[docs]
class LAMB(Optimizer):
r"""Implements the Lamb optimizer from `"Large batch optimization for deep learning: training BERT in 76 minutes"
<https://arxiv.org/pdf/1904.00962v3.pdf>`_.
The estimation of momentums is described as follows, :math:`\forall t \geq 1`:
.. math::
m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\
v_t \leftarrow \beta_2 v_{t-1} + (1 - \beta_2) g_t^2
where :math:`g_t` is the gradient of :math:`\theta_t`,
:math:`\beta_1, \beta_2 \in [0, 1]^3` are the exponential average smoothing coefficients,
:math:`m_0 = 0,\ v_0 = 0`.
Then we correct their biases using:
.. math::
\hat{m_t} \leftarrow \frac{m_t}{1 - \beta_1^t} \\
\hat{v_t} \leftarrow \frac{v_t}{1 - \beta_2^t}
And finally the update step is performed using the following rule:
.. math::
r_t \leftarrow \frac{\hat{m_t}}{\sqrt{\hat{v_t}} + \epsilon} \\
\theta_t \leftarrow \theta_{t-1} - \alpha \phi(\lVert \theta_t \rVert)
\frac{r_t + \lambda \theta_t}{\lVert r_t + \theta_t \rVert}
where :math:`\theta_t` is the parameter value at step :math:`t` (:math:`\theta_0` being the initialization value),
:math:`\phi` is a clipping function,
:math:`\alpha` is the learning rate, :math:`\lambda \geq 0` is the weight decay, :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], optional): beta coefficients used for running averages (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)
scale_clip (tuple, optional): the lower and upper bounds for the weight norm in local LR of LARS
"""
def __init__(
self,
params: Iterable[torch.nn.Parameter],
lr: float = 1e-3,
betas: Tuple[float, float] = (0.9, 0.999),
eps: float = 1e-8,
weight_decay: float = 0.0,
scale_clip: Optional[Tuple[float, float]] = None,
) -> None:
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]}")
defaults = {"lr": lr, "betas": betas, "eps": eps, "weight_decay": weight_decay}
super().__init__(params, defaults)
# LARS arguments
self.scale_clip = scale_clip
if self.scale_clip is None:
self.scale_clip = (0.0, 10.0)
@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:
for p in group["params"]:
if p.grad is None:
continue
grad = p.grad.data
if grad.is_sparse:
raise RuntimeError(f"{self.__class__.__name__} does not support sparse gradients")
state = self.state[p]
# State initialization
if len(state) == 0:
state["step"] = 0
# Exponential moving average of gradient values
state["exp_avg"] = torch.zeros_like(p.data)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(p.data)
exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
beta1, beta2 = group["betas"]
state["step"] += 1
# 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)
# Gradient term correction
update = torch.zeros_like(p.data)
denom = exp_avg_sq.sqrt().add_(group["eps"])
update.addcdiv_(exp_avg, denom)
# Weight decay
if group["weight_decay"] != 0:
update.add_(p.data, alpha=group["weight_decay"])
# LARS
p_norm = p.data.pow(2).sum().sqrt()
update_norm = update.pow(2).sum().sqrt()
phi_p = p_norm.clamp(*self.scale_clip)
# Compute the local LR
local_lr = 1 if phi_p == 0 or update_norm == 0 else phi_p / update_norm
state["local_lr"] = local_lr
p.data.add_(update, alpha=-group["lr"] * local_lr)
return loss