# coding=utf-8
# Copyright 2018 The Google AI Language Team Authors and The HuggingFace Inc. team.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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"""PyTorch optimization for BERT model."""
import math
from typing import Callable, Iterable, Tuple
import torch
from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR
from .utils import logging
logger = logging.get_logger(__name__)
[docs]def get_constant_schedule(optimizer: Optimizer, last_epoch: int = -1):
"""
Create a schedule with a constant learning rate, using the learning rate set in optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
return LambdaLR(optimizer, lambda _: 1, last_epoch=last_epoch)
[docs]def get_constant_schedule_with_warmup(optimizer: Optimizer, num_warmup_steps: int, last_epoch: int = -1):
"""
Create a schedule with a constant learning rate preceded by a warmup period during which the learning rate
increases linearly between 0 and the initial lr set in the optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
def lr_lambda(current_step: int):
if current_step < num_warmup_steps:
return float(current_step) / float(max(1.0, num_warmup_steps))
return 1.0
return LambdaLR(optimizer, lr_lambda, last_epoch=last_epoch)
[docs]def get_linear_schedule_with_warmup(optimizer, num_warmup_steps, num_training_steps, last_epoch=-1):
"""
Create a schedule with a learning rate that decreases linearly from the initial lr set in the optimizer to 0,
after a warmup period during which it increases linearly from 0 to the initial lr set in the optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
num_training_steps (:obj:`int`):
The total number of training steps.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
def lr_lambda(current_step: int):
if current_step < num_warmup_steps:
return float(current_step) / float(max(1, num_warmup_steps))
return max(
0.0, float(num_training_steps - current_step) / float(max(1, num_training_steps - num_warmup_steps))
)
return LambdaLR(optimizer, lr_lambda, last_epoch)
[docs]def get_cosine_schedule_with_warmup(
optimizer: Optimizer, num_warmup_steps: int, num_training_steps: int, num_cycles: float = 0.5, last_epoch: int = -1
):
"""
Create a schedule with a learning rate that decreases following the values of the cosine function between the
initial lr set in the optimizer to 0, after a warmup period during which it increases linearly between 0 and the
initial lr set in the optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
num_training_steps (:obj:`int`):
The total number of training steps.
num_cycles (:obj:`float`, `optional`, defaults to 0.5):
The number of waves in the cosine schedule (the defaults is to just decrease from the max value to 0
following a half-cosine).
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
def lr_lambda(current_step):
if current_step < num_warmup_steps:
return float(current_step) / float(max(1, num_warmup_steps))
progress = float(current_step - num_warmup_steps) / float(max(1, num_training_steps - num_warmup_steps))
return max(0.0, 0.5 * (1.0 + math.cos(math.pi * float(num_cycles) * 2.0 * progress)))
return LambdaLR(optimizer, lr_lambda, last_epoch)
[docs]def get_cosine_with_hard_restarts_schedule_with_warmup(
optimizer: Optimizer, num_warmup_steps: int, num_training_steps: int, num_cycles: int = 1, last_epoch: int = -1
):
"""
Create a schedule with a learning rate that decreases following the values of the cosine function between the
initial lr set in the optimizer to 0, with several hard restarts, after a warmup period during which it increases
linearly between 0 and the initial lr set in the optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
num_training_steps (:obj:`int`):
The total number of training steps.
num_cycles (:obj:`int`, `optional`, defaults to 1):
The number of hard restarts to use.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
def lr_lambda(current_step):
if current_step < num_warmup_steps:
return float(current_step) / float(max(1, num_warmup_steps))
progress = float(current_step - num_warmup_steps) / float(max(1, num_training_steps - num_warmup_steps))
if progress >= 1.0:
return 0.0
return max(0.0, 0.5 * (1.0 + math.cos(math.pi * ((float(num_cycles) * progress) % 1.0))))
return LambdaLR(optimizer, lr_lambda, last_epoch)
def get_polynomial_decay_schedule_with_warmup(
optimizer, num_warmup_steps, num_training_steps, lr_end=1e-7, power=1.0, last_epoch=-1
):
"""
Create a schedule with a learning rate that decreases as a polynomial decay
from the initial lr set in the optimizer to end lr defined by `lr_end`,
after a warmup period during which it increases linearly from 0 to the
initial lr set in the optimizer.
Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
num_training_steps (:obj:`int`):
The total number of training steps.
lr_end (:obj:`float`, `optional`, defaults to 1e-7):
The end LR.
power (:obj:`float`, `optional`, defaults to 1.0):
Power factor.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.
Note: `power` defaults to 1.0 as in the fairseq implementation, which in turn is
based on the original BERT implementation at
https://github.com/google-research/bert/blob/f39e881b169b9d53bea03d2d341b31707a6c052b/optimization.py#L37
Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
"""
lr_init = optimizer.defaults["lr"]
assert lr_init > lr_end, f"lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})"
def lr_lambda(current_step: int):
if current_step < num_warmup_steps:
return float(current_step) / float(max(1, num_warmup_steps))
elif current_step > num_training_steps:
return lr_end / lr_init # as LambdaLR multiplies by lr_init
else:
lr_range = lr_init - lr_end
decay_steps = num_training_steps - num_warmup_steps
pct_remaining = 1 - (current_step - num_warmup_steps) / decay_steps
decay = lr_range * pct_remaining ** power + lr_end
return decay / lr_init # as LambdaLR multiplies by lr_init
return LambdaLR(optimizer, lr_lambda, last_epoch)
[docs]class AdamW(Optimizer):
"""
Implements Adam algorithm with weight decay fix as introduced in
`Decoupled Weight Decay Regularization <https://arxiv.org/abs/1711.05101>`__.
Parameters:
params (:obj:`Iterable[torch.nn.parameter.Parameter]`):
Iterable of parameters to optimize or dictionaries defining parameter groups.
lr (:obj:`float`, `optional`, defaults to 1e-3):
The learning rate to use.
betas (:obj:`Tuple[float,float]`, `optional`, defaults to (0.9, 0.999)):
Adam's betas parameters (b1, b2).
eps (:obj:`float`, `optional`, defaults to 1e-6):
Adam's epsilon for numerical stability.
weight_decay (:obj:`float`, `optional`, defaults to 0):
Decoupled weight decay to apply.
correct_bias (:obj:`bool`, `optional`, defaults to `True`):
Whether ot not to correct bias in Adam (for instance, in Bert TF repository they use :obj:`False`).
"""
def __init__(
self,
params: Iterable[torch.nn.parameter.Parameter],
lr: float = 1e-3,
betas: Tuple[float, float] = (0.9, 0.999),
eps: float = 1e-6,
weight_decay: float = 0.0,
correct_bias: bool = True,
):
if lr < 0.0:
raise ValueError("Invalid learning rate: {} - should be >= 0.0".format(lr))
if not 0.0 <= betas[0] < 1.0:
raise ValueError("Invalid beta parameter: {} - should be in [0.0, 1.0[".format(betas[0]))
if not 0.0 <= betas[1] < 1.0:
raise ValueError("Invalid beta parameter: {} - should be in [0.0, 1.0[".format(betas[1]))
if not 0.0 <= eps:
raise ValueError("Invalid epsilon value: {} - should be >= 0.0".format(eps))
defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, correct_bias=correct_bias)
super().__init__(params, defaults)
[docs] def step(self, closure: Callable = None):
"""
Performs a single optimization step.
Arguments:
closure (:obj:`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.is_sparse:
raise RuntimeError("Adam does not support sparse gradients, please consider SparseAdam instead")
state = self.state[p]
# State initialization
if len(state) == 0:
state["step"] = 0
# Exponential moving average of gradient values
state["exp_avg"] = torch.zeros_like(p.data)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(p.data)
exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
beta1, beta2 = group["betas"]
state["step"] += 1
# Decay the first and second moment running average coefficient
# In-place operations to update the averages at the same time
exp_avg.mul_(beta1).add_(grad, alpha=1.0 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1.0 - beta2)
denom = exp_avg_sq.sqrt().add_(group["eps"])
step_size = group["lr"]
if group["correct_bias"]: # No bias correction for Bert
bias_correction1 = 1.0 - beta1 ** state["step"]
bias_correction2 = 1.0 - beta2 ** state["step"]
step_size = step_size * math.sqrt(bias_correction2) / bias_correction1
p.data.addcdiv_(exp_avg, denom, value=-step_size)
# Just adding the square of the weights to the loss function is *not*
# the correct way of using L2 regularization/weight decay with Adam,
# since that will interact with the m and v parameters in strange ways.
#
# Instead we want to decay the weights in a manner that doesn't interact
# with the m/v parameters. This is equivalent to adding the square
# of the weights to the loss with plain (non-momentum) SGD.
# Add weight decay at the end (fixed version)
if group["weight_decay"] > 0.0:
p.data.add_(p.data, alpha=-group["lr"] * group["weight_decay"])
return loss
[docs]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):
r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=-1, keepdim=True)).rsqrt_()
c_factor = exp_avg_sq_col.rsqrt()
return torch.mm(r_factor.unsqueeze(-1), c_factor.unsqueeze(0))
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)
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
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_(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)
if p.data.dtype in {torch.float16, torch.bfloat16}:
p.data.copy_(p_data_fp32)
return loss