""" AdaHessian Optimizer
Lifted from https://github.com/davda54/ada-hessian/blob/master/ada_hessian.py
Originally licensed MIT, Copyright 2020, David Samuel
"""
import torch
[docs]class Adahessian(torch.optim.Optimizer):
"""
Implements the AdaHessian algorithm from "ADAHESSIAN: An Adaptive Second OrderOptimizer for Machine Learning"
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining parameter groups
lr (float, optional): learning rate (default: 0.1)
betas ((float, float), optional): coefficients used for computing running averages of gradient and the
squared hessian trace (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: 0.0)
hessian_power (float, optional): exponent of the hessian trace (default: 1.0)
update_each (int, optional): compute the hessian trace approximation only after *this* number of steps
(to save time) (default: 1)
n_samples (int, optional): how many times to sample `z` for the approximation of the hessian trace (default: 1)
"""
def __init__(self, params, lr=0.1, betas=(0.9, 0.999), eps=1e-8, weight_decay=0.0,
hessian_power=1.0, update_each=1, n_samples=1, avg_conv_kernel=False):
if 0.0 > lr:
raise ValueError(f"Invalid learning rate: {lr}")
if 0.0 > eps:
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 0.0 <= hessian_power <= 1.0:
raise ValueError(f"Invalid Hessian power value: {hessian_power}")
self.n_samples = n_samples
self.update_each = update_each
self.avg_conv_kernel = avg_conv_kernel
# use a separate generator that deterministically generates the same `z`s across all GPUs in case of distributed training
self.seed = 2147483647
self.generator = torch.Generator().manual_seed(self.seed)
defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, hessian_power=hessian_power)
super(Adahessian, self).__init__(params, defaults)
for p in self.get_params():
p.hess = 0.0
self.state[p]["hessian step"] = 0
@property
def is_second_order(self):
return True
[docs] def get_params(self):
"""
Gets all parameters in all param_groups with gradients
"""
return (p for group in self.param_groups for p in group['params'] if p.requires_grad)
[docs] def zero_hessian(self):
"""
Zeros out the accumalated hessian traces.
"""
for p in self.get_params():
if not isinstance(p.hess, float) and self.state[p]["hessian step"] % self.update_each == 0:
p.hess.zero_()
[docs] @torch.no_grad()
def set_hessian(self):
"""
Computes the Hutchinson approximation of the hessian trace and accumulates it for each trainable parameter.
"""
params = []
for p in filter(lambda p: p.grad is not None, self.get_params()):
if self.state[p]["hessian step"] % self.update_each == 0: # compute the trace only each `update_each` step
params.append(p)
self.state[p]["hessian step"] += 1
if len(params) == 0:
return
if self.generator.device != params[0].device: # hackish way of casting the generator to the right device
self.generator = torch.Generator(params[0].device).manual_seed(self.seed)
grads = [p.grad for p in params]
for i in range(self.n_samples):
# Rademacher distribution {-1.0, 1.0}
zs = [torch.randint(0, 2, p.size(), generator=self.generator, device=p.device) * 2.0 - 1.0 for p in params]
h_zs = torch.autograd.grad(
grads, params, grad_outputs=zs, only_inputs=True, retain_graph=i < self.n_samples - 1)
for h_z, z, p in zip(h_zs, zs, params):
p.hess += h_z * z / self.n_samples # approximate the expected values of z*(H@z)
[docs] @torch.no_grad()
def step(self, closure=None):
"""
Performs a single optimization step.
Arguments:
closure (callable, optional) -- a closure that reevaluates the model and returns the loss (default: None)
"""
loss = None
if closure is not None:
loss = closure()
self.zero_hessian()
self.set_hessian()
for group in self.param_groups:
for p in group['params']:
if p.grad is None or p.hess is None:
continue
if self.avg_conv_kernel and p.dim() == 4:
p.hess = torch.abs(p.hess).mean(dim=[2, 3], keepdim=True).expand_as(p.hess).clone()
# Perform correct stepweight decay as in AdamW
p.mul_(1 - group['lr'] * group['weight_decay'])
state = self.state[p]
# State initialization
if len(state) == 1:
state['step'] = 0
# Exponential moving average of gradient values
state['exp_avg'] = torch.zeros_like(p)
# Exponential moving average of Hessian diagonal square values
state['exp_hessian_diag_sq'] = torch.zeros_like(p)
exp_avg, exp_hessian_diag_sq = state['exp_avg'], state['exp_hessian_diag_sq']
beta1, beta2 = group['betas']
state['step'] += 1
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(p.grad, alpha=1 - beta1)
exp_hessian_diag_sq.mul_(beta2).addcmul_(p.hess, p.hess, value=1 - beta2)
bias_correction1 = 1 - beta1 ** state['step']
bias_correction2 = 1 - beta2 ** state['step']
k = group['hessian_power']
denom = (exp_hessian_diag_sq / bias_correction2).pow_(k / 2).add_(group['eps'])
# make update
step_size = group['lr'] / bias_correction1
p.addcdiv_(exp_avg, denom, value=-step_size)
return loss