# Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # 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. # Most of the code here has been copied from: # https://github.com/pytorch/fairseq/blob/main/fairseq/optim/adafactor.py import math import torch from torch.optim.optimizer import Optimizer __all__ = ['Adafactor'] class Adafactor(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`. Args: 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 constans 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, 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, min_step=1e-2, ): 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") self.min_step = min_step 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, min_step=min_step, ) super(Adafactor, self).__init__(params, defaults) @property def supports_memory_efficient_fp16(self): return True @property def supports_flat_params(self): return False def _get_lr(self, 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 self.min_step 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 def _get_options(self, 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(self, 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. Args: 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) group["lr"] = self._get_lr(group, state) 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_(update.mean(dim=-1), alpha=1.0 - beta2t) 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_(update, alpha=1.0 - beta2t) update = exp_avg_sq.rsqrt().mul_(grad) update.div_((self._rms(update) / group["clip_threshold"]).clamp_(min=1.0)) update.mul_(group["lr"]) if use_first_moment: exp_avg = state["exp_avg"] exp_avg.mul_(group["beta1"]).add_(update, alpha=1 - group["beta1"]) update = exp_avg if group["weight_decay"] != 0: p_data_fp32.add_(p_data_fp32, alpha=-group["weight_decay"] * group["lr"]) p_data_fp32.add_(-update) if p.data.dtype in {torch.float16, torch.bfloat16}: p.data.copy_(p_data_fp32) return loss