# 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 math
import torch
import torch.optim
from . import LegacyFairseqOptimizer, register_optimizer
@register_optimizer("adafactor")
class FairseqAdafactor(LegacyFairseqOptimizer):
def __init__(self, args, params):
super().__init__(args)
self._optimizer = Adafactor(params, **self.optimizer_config)
@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('--weight-decay', '--wd', default=0.0, type=float, metavar='WD',
help='weight decay')
parser.add_argument('--scale-parameter', action='store_true',
help='scale learning rate by root mean square of parameter')
parser.add_argument('--relative-step', action='store_true',
help='set learning rate to inverse square root of timestep,'
'otherwise use external learning rate')
parser.add_argument('--warmup-init', action='store_true',
help='use relative step for warm-up learning rate schedule')
# 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,
"decay_rate": self.args.decay_rate,
"beta1": self.args.beta1,
"weight_decay": self.args.weight_decay,
"scale_parameter": self.args.scale_parameter, # defaults to False
"relative_step": self.args.relative_step, # defaults to False
"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)
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,
):
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(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 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):
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