# 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, Iterable, List, Optional, Tuple
import torch
from torch import Tensor
from torch.nn import functional as F
from torch.optim import Adam
__all__ = ["AdamP", "adamp"]
[docs]
class AdamP(Adam):
r"""Implements the AdamP optimizer from `"AdamP: Slowing Down the Slowdown for Momentum Optimizers on
Scale-invariant Weights" <https://arxiv.org/pdf/2006.08217.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 = g_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::
p_t \leftarrow \frac{\hat{m_t}}{\sqrt{\hat{n_t} + \epsilon}} \\
q_t \leftarrow \begin{cases}
\prod_{\theta_t}(p_t) & if\ cos(\theta_t, g_t) < \delta / \sqrt{dim(\theta)}\\
p_t & \text{otherwise}\\
\end{cases} \\
\theta_t \leftarrow \theta_{t-1} - \alpha q_t
where :math:`\theta_t` is the parameter value at step :math:`t` (:math:`\theta_0` being the initialization value),
:math:`\prod_{\theta_t}(p_t)` is the projection of :math:`p_t` onto the tangent space of :math:`\theta_t`,
:math:`cos(\theta_t, g_t)` is the cosine similarity between :math:`\theta_t` and :math:`g_t`,
:math:`\alpha` is the learning rate, :math:`\delta > 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], 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)
amsgrad (bool, optional): whether to use the AMSGrad variant (default: False)
delta (float, optional): delta threshold for projection (default: False)
"""
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,
delta: float = 0.1,
) -> None:
super().__init__(params, lr, betas, eps, weight_decay, amsgrad)
self.delta = delta
@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 = []
max_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)
# 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)
exp_avgs.append(state["exp_avg"])
exp_avg_sqs.append(state["exp_avg_sq"])
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"])
beta1, beta2 = group["betas"]
adamp(
params_with_grad,
grads,
exp_avgs,
exp_avg_sqs,
max_exp_avg_sqs,
state_steps,
group["amsgrad"],
beta1,
beta2,
group["lr"],
group["weight_decay"],
group["eps"],
self.delta,
)
return loss
def adamp(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
state_steps: List[int],
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
delta: float,
) -> None:
r"""Functional API that performs AdamP algorithm computation.
See :class:`~holocron.optim.AdamP` for details.
"""
for i, param in enumerate(params):
grad = grads[i]
exp_avg = exp_avgs[i]
exp_avg_sq = 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
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
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_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i])
# Use the max. for normalizing running avg. of gradient
denom = (max_exp_avg_sqs[i].sqrt() / math.sqrt(bias_correction2)).add_(eps)
else:
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps)
# Extra step
pt = exp_avg / bias_correction1 / denom
if F.cosine_similarity(param.data.view(1, -1), grad.view(1, -1)).max() < delta / math.sqrt(param.data.numel()):
normalized_param = param.data / param.data.norm().add_(eps)
pt -= (normalized_param * pt).sum() * normalized_param.data
param.add_(pt, alpha=-lr)