# 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.
import math
from typing import Callable, Dict, Iterable, List, Optional, Tuple
import torch
from torch import Tensor
from torch.optim.optimizer import Optimizer
__all__ = ["TAdam", "tadam"]
[docs]
class TAdam(Optimizer):
r"""Implements the TAdam optimizer from `"TAdam: A Robust Stochastic Gradient Optimizer"
<https://arxiv.org/pdf/2003.00179.pdf>`_.
The estimation of momentums is described as follows, :math:`\forall t \geq 1`:
.. math::
w_t \leftarrow (\nu + d) \Big(\nu + \sum\limits_{j}
\frac{(g_t^j - m_{t-1}^j)^2}{v_{t-1} + \epsilon} \Big)^{-1} \\
m_t \leftarrow \frac{W_{t-1}}{W_{t-1} + w_t} m_{t-1} + \frac{w_t}{W_{t-1} + w_t} g_t \\
v_t \leftarrow \beta_2 v_{t-1} + (1 - \beta_2) (g_t - g_{t-1})
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,\ W_0 = \frac{\beta_1}{1 - \beta_1}`;
:math:`\nu` is the degrees of freedom and :math:`d` if the number of dimensions of the parameter gradient.
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::
\theta_t \leftarrow \theta_{t-1} - \alpha \frac{\hat{m_t}}{\sqrt{\hat{v_t}} + \epsilon}
where :math:`\theta_t` is the parameter value at step :math:`t` (:math:`\theta_0` being the initialization value),
:math:`\alpha` is the learning rate, :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): 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)
dof (int, optional): degrees of freedom
"""
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,
amsgrad: bool = False,
dof: Optional[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]}")
if not weight_decay >= 0.0:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = {"lr": lr, "betas": betas, "eps": eps, "weight_decay": weight_decay, "amsgrad": amsgrad, "dof": dof}
super().__init__(params, defaults)
def __setstate__(self, state: Dict[str, torch.Tensor]) -> None:
super().__setstate__(state)
for group in self.param_groups:
group.setdefault("amsgrad", False)
@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_avg_sqs = []
W_ts = [] # noqa: N806
max_exp_avg_sqs = []
state_steps = []
beta1, beta2 = group["betas"]
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)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(p, memory_format=torch.preserve_format)
if group["amsgrad"]:
# Maintains max of all exp. moving avg. of sq. grad. values
state["max_exp_avg_sq"] = torch.zeros_like(p, memory_format=torch.preserve_format)
# Tadam specific
state["W_t"] = beta1 / (1 - beta1) * torch.ones(1, dtype=p.data.dtype, device=p.data.device)
exp_avgs.append(state["exp_avg"])
exp_avg_sqs.append(state["exp_avg_sq"])
W_ts.append(state["W_t"])
if group["amsgrad"]:
max_exp_avg_sqs.append(state["max_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"])
tadam(
params_with_grad,
grads,
exp_avgs,
exp_avg_sqs,
max_exp_avg_sqs,
W_ts,
state_steps,
group["amsgrad"],
beta1,
beta2,
group["lr"],
group["weight_decay"],
group["eps"],
group["dof"],
)
return loss
def tadam(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
W_ts: List[Tensor], # noqa: N803
state_steps: List[int],
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
dof: float,
) -> None:
r"""Functional API that performs TAdam algorithm computation.
See :class:`~holocron.optim.TAdam` for details.
"""
for i, param in enumerate(params):
grad = grads[i]
exp_avg = exp_avgs[i]
exp_avg_sq = exp_avg_sqs[i]
W_t = W_ts[i] # noqa: N806
_dof = param.data.numel() if dof is None else dof
step = state_steps[i]
if amsgrad:
max_exp_avg_sq = max_exp_avg_sqs[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
w_t = grad.sub(exp_avg).pow_(2).div_(exp_avg_sq.add(eps)).sum()
w_t.add_(_dof).pow_(-1).mul_(_dof + param.data.numel())
exp_avg.mul_(W_t / (W_t + w_t)).addcdiv_(w_t * grad, W_t + w_t)
W_t.mul_((2 * beta1 - 1) / beta1)
W_t.add_(w_t)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.maximum(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom = (max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps)
else:
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps)
step_size = lr / bias_correction1
param.addcdiv_(exp_avg, denom, value=-step_size)