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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)
@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)
# 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 |