Source code for pywick.optimizers.adahessian

""" AdaHessian Optimizer

Lifted from
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