| | """ Adafactor Optimizer |
| | |
| | Lifted from https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py |
| | |
| | Original header/copyright below. |
| | |
| | """ |
| | |
| | |
| | |
| | |
| | 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] |
| | ) |
| | 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) |
| |
|
| | @staticmethod |
| | 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"] |
| |
|
| | @staticmethod |
| | 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 |
| |
|
| | @staticmethod |
| | 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) |
| | |
| | if len(state) == 0: |
| | state["step"] = 0 |
| |
|
| | if use_first_moment: |
| | |
| | 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)) |
| | |
| | |
| |
|
| | |
| | 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) |
| | |
| | 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) |
| | |
| | update = exp_avg |
| |
|
| | if group["weight_decay"] != 0: |
| | p_data_fp32.add_(-group["weight_decay"] * lr_t, p_data_fp32) |
| | |
| |
|
| | p_data_fp32.add_(-update) |
| |
|
| | if p.data.dtype in {torch.float16, torch.bfloat16}: |
| | p.data.copy_(p_data_fp32) |
| |
|
| | return loss |
| |
|