optimizers.py

import math

import torch
from torch.optim import Optimizer


class Adafactor(Optimizer):
    """
    AdaFactor pytorch implementation can be used as a drop in replacement for Adam original fairseq code:
    https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py
    Paper: `Adafactor: Adaptive Learning Rates with Sublinear Memory Cost` 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 (:obj:`Iterable[torch.nn.parameter.Parameter]`):
            Iterable of parameters to optimize or dictionaries defining parameter groups.
        lr (:obj:`float`, `optional`):
            The external learning rate.
        eps (:obj:`Tuple[float, float]`, `optional`, defaults to (1e-30, 1e-3)):
            Regularization constants for square gradient and parameter scale respectively
        clip_threshold (:obj:`float`, `optional`, defaults 1.0):
            Threshold of root mean square of final gradient update
        decay_rate (:obj:`float`, `optional`, defaults to -0.8):
            Coefficient used to compute running averages of square
        beta1 (:obj:`float`, `optional`):
            Coefficient used for computing running averages of gradient
        weight_decay (:obj:`float`, `optional`, defaults to 0):
            Weight decay (L2 penalty)
        scale_parameter (:obj:`bool`, `optional`, defaults to :obj:`True`):
            If True, learning rate is scaled by root mean square
        relative_step (:obj:`bool`, `optional`, defaults to :obj:`True`):
            If True, time-dependent learning rate is computed instead of external learning rate
        warmup_init (:obj:`bool`, `optional`, defaults to :obj:`False`):
            Time-dependent learning rate computation depends on whether warm-up initialization is being used
    This implementation handles low-precision (FP16, bfloat) values, but we have not thoroughly tested.
    Recommended T5 finetuning settings:
        - Scheduled LR warm-up to fixed LR
        - disable relative updates
        - use clip threshold: https://arxiv.org/abs/2004.14546
        Example::
            Adafactor(model.parameters(), lr=1e-3, relative_step=False, warmup_init=True)
        - Alternatively, relative_step with warmup_init can be used.
        - Training without LR warmup or clip threshold is not recommended. Additional optimizer operations like
          gradient clipping should not be used alongside Adafactor.
    Usage::
        # replace AdamW with Adafactor
        optimizer = Adafactor(
            model.parameters(),
            lr=1e-3,
            eps=(1e-30, 1e-3),
            clip_threshold=1.0,
            decay_rate=-0.8,
            beta1=None,
            weight_decay=0.0,
            relative_step=False,
            scale_parameter=False,
            warmup_init=False
        )
    """

    def __init__(
        self,
        params,
        lr=None,
        eps=(1e-30, 1e-3),
        clip_threshold=1.0,
        decay_rate=-0.8,
        beta1=None,
        weight_decay=0.0,
        scale_parameter=True,
        relative_step=True,
        warmup_init=False,
    ):
        if lr is not None and relative_step:
            raise ValueError("Cannot combine manual lr and relative_step options")
        if warmup_init and not relative_step:
            raise ValueError("warmup_init requires relative_step=True")

        defaults = dict(
            lr=lr,
            eps=eps,
            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().__init__(params, defaults)

    @staticmethod
    def _get_lr(param_group, param_state):
        rel_step_sz = param_group["lr"]
        if param_group["relative_step"]:
            min_step = 1e-6 * param_state["step"] if param_group["warmup_init"] else 1e-2
            rel_step_sz = 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"][1], param_state["RMS"])
        return param_scale * rel_step_sz

    @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)

    @staticmethod
    def _approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col):
        # copy from fairseq's adafactor implementation:
        # https://github.com/huggingface/transformers/blob/8395f14de6068012787d83989c3627c3df6a252b/src/transformers/optimization.py#L505
        # fixes gradient ckpt and 3-d parralelism issues huggingface/transformers#11536
        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 = self._get_lr(group, state)
                group['scaled_lr'] = lr.item() if isinstance(lr, torch.Tensor) else lr

                beta2t = 1.0 - math.pow(state["step"], group["decay_rate"])
                update = (grad ** 2) + group["eps"][0]
                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))

                    # 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)
                    update = exp_avg_sq.rsqrt().mul_(grad)

                update.div_((self._rms(update) / group["clip_threshold"]).clamp_(min=1.0))
                update.mul_(lr)

                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, 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