# Source: https://github.com/jettify/pytorch-optimizer/blob/master/torch_optimizer/apollo.py (apache 2.0)
import torch
from torch.optim.optimizer import Optimizer
from .a2grad import OptFloat, OptLossClosure, Params
__all__ = 'Apollo'
[docs]class Apollo(Optimizer):
r"""Implements Apollo Optimizer Algorithm.
It has been proposed in `Apollo: An Adaptive Parameter-wise Diagonal
Quasi-Newton Method for Nonconvex Stochastic Optimization`__.
Arguments:
params: iterable of parameters to optimize or dicts defining
parameter groups
lr: learning rate (default: 1e-2)
beta: coefficient used for computing
running averages of gradient (default: 0.9)
eps: term added to the denominator to improve
numerical stability (default: 1e-4)
warmup: number of warmup steps (default: 0)
init_lr: initial learning rate for warmup (default: 0.01)
weight_decay: weight decay (L2 penalty) (default: 0)
__ https://arxiv.org/abs/2009.13586
Note:
Reference code: https://github.com/XuezheMax/apollo
"""
def __init__(
self,
params: Params,
lr: float = 1e-2,
beta: float = 0.9,
eps: float = 1e-4,
warmup: int = 0,
init_lr: float = 0.01,
weight_decay: float = 0,
):
if lr <= 0.0:
raise ValueError('Invalid learning rate: {}'.format(lr))
if eps < 0.0:
raise ValueError('Invalid epsilon value: {}'.format(eps))
if not 0.0 <= beta < 1.0:
raise ValueError('Invalid beta parameter: {}'.format(beta))
if 0.0 > weight_decay:
raise ValueError(
'Invalid weight_decay value: {}'.format(weight_decay)
)
if 0.0 > warmup:
raise ValueError('Invalid warmup updates: {}'.format(warmup))
if not 0.0 <= init_lr <= 1.0:
raise ValueError(
'Invalid initial learning rate: {}'.format(init_lr)
)
defaults = dict(
lr=lr,
beta=beta,
eps=eps,
warmup=warmup,
init_lr=init_lr,
base_lr=lr,
weight_decay=weight_decay,
)
super(Apollo, self).__init__(params, defaults)
[docs] def step(self, closure: OptLossClosure = None) -> OptFloat:
r"""Performs a single optimization step.
Arguments:
closure: A closure that reevaluates the model and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
state = self.state[p]
# State initialization
if len(state) == 0:
state['step'] = 0
# Exponential moving average of gradient values
state['exp_avg_grad'] = torch.zeros_like(
p, memory_format=torch.preserve_format
)
# Exponential moving average of squared gradient values
state['approx_hessian'] = torch.zeros_like(
p, memory_format=torch.preserve_format
)
# Previous update direction
state['update'] = torch.zeros_like(
p, memory_format=torch.preserve_format
)
# Calculate current lr
if state['step'] < group['warmup']:
curr_lr = (group['base_lr'] - group['init_lr']) * state[
'step'
] / group['warmup'] + group['init_lr']
else:
curr_lr = group['lr']
# Perform optimization step
grad = p.grad.data
if grad.is_sparse:
raise RuntimeError(
'Atom does not support sparse gradients.'
)
# Perform step weight decay
if group['weight_decay'] != 0:
grad = grad.add(p, alpha=group['weight_decay'])
beta = group['beta']
exp_avg_grad = state['exp_avg_grad']
B = state['approx_hessian']
d_p = state['update']
state['step'] += 1
bias_correction = 1 - beta ** state['step']
alpha = (1 - beta) / bias_correction
# Update the running average grad
delta_grad = grad - exp_avg_grad
exp_avg_grad.add_(delta_grad, alpha=alpha)
denom = d_p.norm(p=4).add(group['eps'])
d_p.div_(denom)
v_sq = d_p.mul(d_p)
delta = (
delta_grad.div_(denom).mul_(d_p).sum().mul(-alpha)
- B.mul(v_sq).sum()
)
# Update B
B.addcmul_(v_sq, delta)
# calc direction of parameter updates
denom = B.abs().clamp_(min=1)
d_p.copy_(exp_avg_grad.div(denom))
p.data.add_(d_p, alpha=-curr_lr)
return loss