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| """ Adafactor Optimizer | |
| Lifted from https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py | |
| Original header/copyright below. | |
| """ | |
| # Copyright (c) Facebook, Inc. and its affiliates. | |
| # | |
| # This source code is licensed under the MIT license found in the | |
| # LICENSE file in the root directory of this source tree. | |
| import torch | |
| import math | |
| class Adafactor(torch.optim.Optimizer): | |
| """Implements Adafactor algorithm. | |
| This implementation is based on: `Adafactor: Adaptive Learning Rates with Sublinear Memory Cost` | |
| (see https://arxiv.org/abs/1804.04235) | |
| Note that this optimizer internally adjusts the learning rate depending on the | |
| *scale_parameter*, *relative_step* and *warmup_init* options. | |
| To use a manual (external) learning rate schedule you should set `scale_parameter=False` and | |
| `relative_step=False`. | |
| Arguments: | |
| params (iterable): iterable of parameters to optimize or dicts defining parameter groups | |
| lr (float, optional): external learning rate (default: None) | |
| eps (tuple[float, float]): regularization constants for square gradient | |
| and parameter scale respectively (default: (1e-30, 1e-3)) | |
| clip_threshold (float): threshold of root mean square of final gradient update (default: 1.0) | |
| decay_rate (float): coefficient used to compute running averages of square gradient (default: -0.8) | |
| beta1 (float): coefficient used for computing running averages of gradient (default: None) | |
| weight_decay (float, optional): weight decay (L2 penalty) (default: 0) | |
| scale_parameter (bool): if True, learning rate is scaled by root mean square of parameter (default: True) | |
| relative_step (bool): if True, time-dependent learning rate is computed | |
| instead of external learning rate (default: True) | |
| warmup_init (bool): time-dependent learning rate computation depends on | |
| whether warm-up initialization is being used (default: False) | |
| """ | |
| def __init__(self, params, lr=None, eps=1e-30, eps_scale=1e-3, clip_threshold=1.0, | |
| decay_rate=-0.8, betas=None, weight_decay=0.0, scale_parameter=True, warmup_init=False): | |
| relative_step = lr is None | |
| if warmup_init and not relative_step: | |
| raise ValueError('warmup_init requires relative_step=True') | |
| beta1 = None if betas is None else betas[0] # make it compat with standard betas arg | |
| defaults = dict(lr=lr, eps=eps, eps_scale=eps_scale, clip_threshold=clip_threshold, decay_rate=decay_rate, | |
| beta1=beta1, weight_decay=weight_decay, scale_parameter=scale_parameter, | |
| relative_step=relative_step, warmup_init=warmup_init) | |
| super(Adafactor, self).__init__(params, defaults) | |
| def _get_lr(param_group, param_state): | |
| if param_group['relative_step']: | |
| min_step = 1e-6 * param_state['step'] if param_group['warmup_init'] else 1e-2 | |
| lr_t = min(min_step, 1.0 / math.sqrt(param_state['step'])) | |
| param_scale = 1.0 | |
| if param_group['scale_parameter']: | |
| param_scale = max(param_group['eps_scale'], param_state['RMS']) | |
| param_group['lr'] = lr_t * param_scale | |
| return param_group['lr'] | |
| def _get_options(param_group, param_shape): | |
| factored = len(param_shape) >= 2 | |
| use_first_moment = param_group['beta1'] is not None | |
| return factored, use_first_moment | |
| def _rms(tensor): | |
| return tensor.norm(2) / (tensor.numel() ** 0.5) | |
| def _approx_sq_grad(self, exp_avg_sq_row, exp_avg_sq_col): | |
| r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=-1, keepdim=True)).rsqrt_().unsqueeze(-1) | |
| c_factor = exp_avg_sq_col.unsqueeze(-2).rsqrt() | |
| return torch.mul(r_factor, c_factor) | |
| def step(self, closure=None): | |
| """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: | |
| loss = closure() | |
| for group in self.param_groups: | |
| for p in group['params']: | |
| if p.grad is None: | |
| continue | |
| grad = p.grad.data | |
| if grad.dtype in {torch.float16, torch.bfloat16}: | |
| grad = grad.float() | |
| if grad.is_sparse: | |
| raise RuntimeError('Adafactor does not support sparse gradients.') | |
| state = self.state[p] | |
| grad_shape = grad.shape | |
| factored, use_first_moment = self._get_options(group, grad_shape) | |
| # State Initialization | |
| if len(state) == 0: | |
| state['step'] = 0 | |
| if use_first_moment: | |
| # Exponential moving average of gradient values | |
| state['exp_avg'] = torch.zeros_like(grad) | |
| if factored: | |
| state['exp_avg_sq_row'] = torch.zeros(grad_shape[:-1]).to(grad) | |
| state['exp_avg_sq_col'] = torch.zeros(grad_shape[:-2] + grad_shape[-1:]).to(grad) | |
| else: | |
| state['exp_avg_sq'] = torch.zeros_like(grad) | |
| state['RMS'] = 0 | |
| else: | |
| if use_first_moment: | |
| state['exp_avg'] = state['exp_avg'].to(grad) | |
| if factored: | |
| state['exp_avg_sq_row'] = state['exp_avg_sq_row'].to(grad) | |
| state['exp_avg_sq_col'] = state['exp_avg_sq_col'].to(grad) | |
| else: | |
| state['exp_avg_sq'] = state['exp_avg_sq'].to(grad) | |
| p_data_fp32 = p.data | |
| if p.data.dtype in {torch.float16, torch.bfloat16}: | |
| p_data_fp32 = p_data_fp32.float() | |
| state['step'] += 1 | |
| state['RMS'] = self._rms(p_data_fp32) | |
| lr_t = self._get_lr(group, state) | |
| beta2t = 1.0 - math.pow(state['step'], group['decay_rate']) | |
| update = grad ** 2 + group['eps'] | |
| if factored: | |
| exp_avg_sq_row = state['exp_avg_sq_row'] | |
| exp_avg_sq_col = state['exp_avg_sq_col'] | |
| exp_avg_sq_row.mul_(beta2t).add_(1.0 - beta2t, update.mean(dim=-1)) | |
| exp_avg_sq_col.mul_(beta2t).add_(1.0 - beta2t, update.mean(dim=-2)) | |
| #exp_avg_sq_row.mul_(beta2t).add_(update.mean(dim=-1), alpha=1.0 - beta2t) # pytorch 1.6+ | |
| #exp_avg_sq_col.mul_(beta2t).add_(update.mean(dim=-2), alpha=1.0 - beta2t) | |
| # Approximation of exponential moving average of square of gradient | |
| update = self._approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col) | |
| update.mul_(grad) | |
| else: | |
| exp_avg_sq = state['exp_avg_sq'] | |
| exp_avg_sq.mul_(beta2t).add_(1.0 - beta2t, update) | |
| #exp_avg_sq.mul_(beta2t).add_(update, alpha=1.0 - beta2t) # pytorch 1.6+ | |
| update = exp_avg_sq.rsqrt().mul_(grad) | |
| update.div_((self._rms(update) / group['clip_threshold']).clamp_(min=1.0)) | |
| update.mul_(lr_t) | |
| if use_first_moment: | |
| exp_avg = state['exp_avg'] | |
| exp_avg.mul_(group["beta1"]).add_(1 - group["beta1"], update) | |
| #exp_avg.mul_(group['beta1']).add_(update, alpha=1 - group['beta1']) # pytorch 1.6+ | |
| update = exp_avg | |
| if group['weight_decay'] != 0: | |
| p_data_fp32.add_(-group["weight_decay"] * lr_t, p_data_fp32) | |
| #p_data_fp32.add_(p_data_fp32, alpha=-group['weight_decay'] * lr_t) # pytorch 1.6+ | |
| p_data_fp32.add_(-update) | |
| if p.data.dtype in {torch.float16, torch.bfloat16}: | |
| p.data.copy_(p_data_fp32) | |
| return loss |