# Copyright (c) 2017-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the LICENSE file in
# the root directory of this source tree. An additional grant of patent rights
# can be found in the PATENTS file in the same directory.
import math
import torch
import torch.optim
from . import FairseqOptimizer, register_optimizer
[docs]@register_optimizer('adafactor')
class FairseqAdafactor(FairseqOptimizer):
def __init__(self, args, params):
super().__init__(args, params)
self._optimizer = Adafactor(params, **self.optimizer_config)
[docs] @staticmethod
def add_args(parser):
"""Add optimizer-specific arguments to the parser."""
# fmt: off
parser.add_argument('--adafactor-eps', default='(1e-30, 1e-3)', metavar="E",
help='epsilons for Adafactor optimizer')
parser.add_argument('--clip-threshold', type=float, default=1.0, metavar="C",
help='threshold for clipping update root mean square')
parser.add_argument('--decay-rate', type=float, default=-0.8, metavar="D",
help='decay rate of the second moment estimator')
parser.add_argument('--beta1', type=float, default=None, metavar="B",
help='beta for first moment estimator. Optional')
parser.add_argument('--scale-parameter', action='store_true',
help='scale learning rate by root mean square of parameter.')
parser.add_argument('--weight-decay', '--wd', default=0.0, type=float, metavar='WD',
help='weight decay')
parser.add_argument('--warmup-init', action='store_true',
help='use relative step for warm-up learning rate schedule')
parser.add_argument('--relative-step', action='store_true',
help='set learning rate to inverse square root of timestep.'
'If false, external learning rate applied')
# fmt: on
@property
def optimizer_config(self):
"""
Return a kwarg dictionary that will be used to override optimizer
args stored in checkpoints. This allows us to load a checkpoint and
resume training using a different set of optimizer args, e.g., with a
different learning rate.
Note : Convergence issues empirically observed with fp16 on.
Might require search for appropriate configuration.
"""
return {
'lr': self.args.lr[0],
'eps': eval(self.args.adafactor_eps),
'clip_threshold': self.args.clip_threshold,
'beta1': self.args.beta1,
'decay_rate': self.args.decay_rate,
'scale_parameter': self.args.scale_parameter,
'weight_decay': self.args.weight_decay,
'relative_step': self.args.relative_step,
'warmup_init': self.args.warmup_init,
}
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)
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 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):
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(Adafactor, self).__init__(params, defaults)
@property
def supports_memory_efficient_fp16(self):
return True
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 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
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, output):
r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=-1)).rsqrt_().unsqueeze(-1)
c_factor = exp_avg_sq_col.unsqueeze(-2).rsqrt()
torch.mul(r_factor, c_factor, out=output)
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.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]).type_as(grad)
state['exp_avg_sq_col'] = torch.zeros(grad_shape[:-2] + grad_shape[-1:]).type_as(grad)
else:
state['exp_avg_sq'] = torch.zeros_like(grad)
state['RMS'] = 0
else:
if use_first_moment:
state['exp_avg'] = state['exp_avg'].type_as(grad)
if factored:
state['exp_avg_sq_row'] = state['exp_avg_sq_row'].type_as(grad)
state['exp_avg_sq_col'] = state['exp_avg_sq_col'].type_as(grad)
else:
state['exp_avg_sq'] = state['exp_avg_sq'].type_as(grad)
p_data_fp32 = p.data.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_(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
self._approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col, update)
update.mul_(grad)
else:
exp_avg_sq = state['exp_avg_sq']
exp_avg_sq.mul_(beta2t).add_(1.0 - beta2t, update)
torch.rsqrt(exp_avg_sq, out=update).mul_(grad)
update.div_(max(1.0, self._rms(update) / group['clip_threshold']))
update.mul_(group['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'] * group['lr'], p_data_fp32)
p_data_fp32.add_(-update)
p.data.copy_(p_data_fp32)
return loss