import types
import math
from torch._six import inf
from functools import wraps
import warnings
import weakref
from bisect import bisect_right
from .optimizer import Optimizer
class _LRScheduler(object):
def __init__(self, optimizer, last_epoch=-1):
if not isinstance(optimizer, Optimizer):
raise TypeError('{} is not an Optimizer'.format(
type(optimizer).__name__))
self.optimizer = optimizer
if last_epoch == -1:
for group in optimizer.param_groups:
group.setdefault('initial_lr', group['lr'])
last_epoch = 0
else:
for i, group in enumerate(optimizer.param_groups):
if 'initial_lr' not in group:
raise KeyError("param 'initial_lr' is not specified "
"in param_groups[{}] when resuming an optimizer".format(i))
self.base_lrs = list(map(lambda group: group['initial_lr'], optimizer.param_groups))
self.last_epoch = last_epoch
# Following https://github.com/pytorch/pytorch/issues/20124
# We would like to ensure that `lr_scheduler.step()` is called after
# `optimizer.step()`
def with_counter(method):
if getattr(method, '_with_counter', False):
# `optimizer.step()` has already been replaced, return.
return method
# Keep a weak reference to the optimizer instance to prevent
# cyclic references.
instance_ref = weakref.ref(method.__self__)
# Get the unbound method for the same purpose.
func = method.__func__
cls = instance_ref().__class__
del method
@wraps(func)
def wrapper(*args, **kwargs):
instance = instance_ref()
instance._step_count += 1
wrapped = func.__get__(instance, cls)
return wrapped(*args, **kwargs)
# Note that the returned function here is no longer a bound method,
# so attributes like `__func__` and `__self__` no longer exist.
wrapper._with_counter = True
return wrapper
self.optimizer.step = with_counter(self.optimizer.step)
self.optimizer._step_count = 0
self._step_count = 0
self.step(last_epoch)
def state_dict(self):
"""Returns the state of the scheduler as a :class:`dict`.
It contains an entry for every variable in self.__dict__ which
is not the optimizer.
"""
return {key: value for key, value in self.__dict__.items() if key != 'optimizer'}
def load_state_dict(self, state_dict):
"""Loads the schedulers state.
Arguments:
state_dict (dict): scheduler state. Should be an object returned
from a call to :meth:`state_dict`.
"""
self.__dict__.update(state_dict)
def get_lr(self):
raise NotImplementedError
def step(self, epoch=None):
# Raise a warning if old pattern is detected
# https://github.com/pytorch/pytorch/issues/20124
if self._step_count == 1:
if not hasattr(self.optimizer.step, "_with_counter"):
warnings.warn("Seems like `optimizer.step()` has been overridden after learning rate scheduler "
"initialization. Please, make sure to call `optimizer.step()` before "
"`lr_scheduler.step()`. See more details at "
"https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate", UserWarning)
# Just check if there were two first lr_scheduler.step() calls before optimizer.step()
elif self.optimizer._step_count < 1:
warnings.warn("Detected call of `lr_scheduler.step()` before `optimizer.step()`. "
"In PyTorch 1.1.0 and later, you should call them in the opposite order: "
"`optimizer.step()` before `lr_scheduler.step()`. Failure to do this "
"will result in PyTorch skipping the first value of the learning rate schedule."
"See more details at "
"https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate", UserWarning)
self._step_count += 1
if epoch is None:
epoch = self.last_epoch + 1
self.last_epoch = epoch
for param_group, lr in zip(self.optimizer.param_groups, self.get_lr()):
param_group['lr'] = lr
[docs]class LambdaLR(_LRScheduler):
"""Sets the learning rate of each parameter group to the initial lr
times a given function. When last_epoch=-1, sets initial lr as lr.
Args:
optimizer (Optimizer): Wrapped optimizer.
lr_lambda (function or list): A function which computes a multiplicative
factor given an integer parameter epoch, or a list of such
functions, one for each group in optimizer.param_groups.
last_epoch (int): The index of last epoch. Default: -1.
Example:
>>> # Assuming optimizer has two groups.
>>> lambda1 = lambda epoch: epoch // 30
>>> lambda2 = lambda epoch: 0.95 ** epoch
>>> scheduler = LambdaLR(optimizer, lr_lambda=[lambda1, lambda2])
>>> for epoch in range(100):
>>> train(...)
>>> validate(...)
>>> scheduler.step()
"""
def __init__(self, optimizer, lr_lambda, last_epoch=-1):
self.optimizer = optimizer
if not isinstance(lr_lambda, list) and not isinstance(lr_lambda, tuple):
self.lr_lambdas = [lr_lambda] * len(optimizer.param_groups)
else:
if len(lr_lambda) != len(optimizer.param_groups):
raise ValueError("Expected {} lr_lambdas, but got {}".format(
len(optimizer.param_groups), len(lr_lambda)))
self.lr_lambdas = list(lr_lambda)
self.last_epoch = last_epoch
super(LambdaLR, self).__init__(optimizer, last_epoch)
[docs] def state_dict(self):
"""Returns the state of the scheduler as a :class:`dict`.
It contains an entry for every variable in self.__dict__ which
is not the optimizer.
The learning rate lambda functions will only be saved if they are callable objects
and not if they are functions or lambdas.
"""
state_dict = {key: value for key, value in self.__dict__.items() if key not in ('optimizer', 'lr_lambdas')}
state_dict['lr_lambdas'] = [None] * len(self.lr_lambdas)
for idx, fn in enumerate(self.lr_lambdas):
if not isinstance(fn, types.FunctionType):
state_dict['lr_lambdas'][idx] = fn.__dict__.copy()
return state_dict
[docs] def load_state_dict(self, state_dict):
"""Loads the schedulers state.
Arguments:
state_dict (dict): scheduler state. Should be an object returned
from a call to :meth:`state_dict`.
"""
lr_lambdas = state_dict.pop('lr_lambdas')
self.__dict__.update(state_dict)
for idx, fn in enumerate(lr_lambdas):
if fn is not None:
self.lr_lambdas[idx].__dict__.update(fn)
def get_lr(self):
return [base_lr * lmbda(self.last_epoch)
for lmbda, base_lr in zip(self.lr_lambdas, self.base_lrs)]
[docs]class StepLR(_LRScheduler):
"""Sets the learning rate of each parameter group to the initial lr
decayed by gamma every step_size epochs. When last_epoch=-1, sets
initial lr as lr.
Args:
optimizer (Optimizer): Wrapped optimizer.
step_size (int): Period of learning rate decay.
gamma (float): Multiplicative factor of learning rate decay.
Default: 0.1.
last_epoch (int): The index of last epoch. Default: -1.
Example:
>>> # Assuming optimizer uses lr = 0.05 for all groups
>>> # lr = 0.05 if epoch < 30
>>> # lr = 0.005 if 30 <= epoch < 60
>>> # lr = 0.0005 if 60 <= epoch < 90
>>> # ...
>>> scheduler = StepLR(optimizer, step_size=30, gamma=0.1)
>>> for epoch in range(100):
>>> train(...)
>>> validate(...)
>>> scheduler.step()
"""
def __init__(self, optimizer, step_size, gamma=0.1, last_epoch=-1):
self.step_size = step_size
self.gamma = gamma
super(StepLR, self).__init__(optimizer, last_epoch)
def get_lr(self):
return [base_lr * self.gamma ** (self.last_epoch // self.step_size)
for base_lr in self.base_lrs]
[docs]class MultiStepLR(_LRScheduler):
"""Set the learning rate of each parameter group to the initial lr decayed
by gamma once the number of epoch reaches one of the milestones. When
last_epoch=-1, sets initial lr as lr.
Args:
optimizer (Optimizer): Wrapped optimizer.
milestones (list): List of epoch indices. Must be increasing.
gamma (float): Multiplicative factor of learning rate decay.
Default: 0.1.
last_epoch (int): The index of last epoch. Default: -1.
Example:
>>> # Assuming optimizer uses lr = 0.05 for all groups
>>> # lr = 0.05 if epoch < 30
>>> # lr = 0.005 if 30 <= epoch < 80
>>> # lr = 0.0005 if epoch >= 80
>>> scheduler = MultiStepLR(optimizer, milestones=[30,80], gamma=0.1)
>>> for epoch in range(100):
>>> train(...)
>>> validate(...)
>>> scheduler.step()
"""
def __init__(self, optimizer, milestones, gamma=0.1, last_epoch=-1):
if not list(milestones) == sorted(milestones):
raise ValueError('Milestones should be a list of'
' increasing integers. Got {}', milestones)
self.milestones = milestones
self.gamma = gamma
super(MultiStepLR, self).__init__(optimizer, last_epoch)
def get_lr(self):
return [base_lr * self.gamma ** bisect_right(self.milestones, self.last_epoch)
for base_lr in self.base_lrs]
[docs]class ExponentialLR(_LRScheduler):
"""Set the learning rate of each parameter group to the initial lr decayed
by gamma every epoch. When last_epoch=-1, sets initial lr as lr.
Args:
optimizer (Optimizer): Wrapped optimizer.
gamma (float): Multiplicative factor of learning rate decay.
last_epoch (int): The index of last epoch. Default: -1.
"""
def __init__(self, optimizer, gamma, last_epoch=-1):
self.gamma = gamma
super(ExponentialLR, self).__init__(optimizer, last_epoch)
def get_lr(self):
return [base_lr * self.gamma ** self.last_epoch
for base_lr in self.base_lrs]
[docs]class CosineAnnealingLR(_LRScheduler):
r"""Set the learning rate of each parameter group using a cosine annealing
schedule, where :math:`\eta_{max}` is set to the initial lr and
:math:`T_{cur}` is the number of epochs since the last restart in SGDR:
.. math::
\eta_t = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})(1 +
\cos(\frac{T_{cur}}{T_{max}}\pi))
When last_epoch=-1, sets initial lr as lr.
It has been proposed in
`SGDR: Stochastic Gradient Descent with Warm Restarts`_. Note that this only
implements the cosine annealing part of SGDR, and not the restarts.
Args:
optimizer (Optimizer): Wrapped optimizer.
T_max (int): Maximum number of iterations.
eta_min (float): Minimum learning rate. Default: 0.
last_epoch (int): The index of last epoch. Default: -1.
.. _SGDR\: Stochastic Gradient Descent with Warm Restarts:
https://arxiv.org/abs/1608.03983
"""
def __init__(self, optimizer, T_max, eta_min=0, last_epoch=-1):
self.T_max = T_max
self.eta_min = eta_min
super(CosineAnnealingLR, self).__init__(optimizer, last_epoch)
def get_lr(self):
return [self.eta_min + (base_lr - self.eta_min) *
(1 + math.cos(math.pi * self.last_epoch / self.T_max)) / 2
for base_lr in self.base_lrs]
[docs]class ReduceLROnPlateau(object):
"""Reduce learning rate when a metric has stopped improving.
Models often benefit from reducing the learning rate by a factor
of 2-10 once learning stagnates. This scheduler reads a metrics
quantity and if no improvement is seen for a 'patience' number
of epochs, the learning rate is reduced.
Args:
optimizer (Optimizer): Wrapped optimizer.
mode (str): One of `min`, `max`. In `min` mode, lr will
be reduced when the quantity monitored has stopped
decreasing; in `max` mode it will be reduced when the
quantity monitored has stopped increasing. Default: 'min'.
factor (float): Factor by which the learning rate will be
reduced. new_lr = lr * factor. Default: 0.1.
patience (int): Number of epochs with no improvement after
which learning rate will be reduced. For example, if
`patience = 2`, then we will ignore the first 2 epochs
with no improvement, and will only decrease the LR after the
3rd epoch if the loss still hasn't improved then.
Default: 10.
verbose (bool): If ``True``, prints a message to stdout for
each update. Default: ``False``.
threshold (float): Threshold for measuring the new optimum,
to only focus on significant changes. Default: 1e-4.
threshold_mode (str): One of `rel`, `abs`. In `rel` mode,
dynamic_threshold = best * ( 1 + threshold ) in 'max'
mode or best * ( 1 - threshold ) in `min` mode.
In `abs` mode, dynamic_threshold = best + threshold in
`max` mode or best - threshold in `min` mode. Default: 'rel'.
cooldown (int): Number of epochs to wait before resuming
normal operation after lr has been reduced. Default: 0.
min_lr (float or list): A scalar or a list of scalars. A
lower bound on the learning rate of all param groups
or each group respectively. Default: 0.
eps (float): Minimal decay applied to lr. If the difference
between new and old lr is smaller than eps, the update is
ignored. Default: 1e-8.
Example:
>>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
>>> scheduler = ReduceLROnPlateau(optimizer, 'min')
>>> for epoch in range(10):
>>> train(...)
>>> val_loss = validate(...)
>>> # Note that step should be called after validate()
>>> scheduler.step(val_loss)
"""
def __init__(self, optimizer, mode='min', factor=0.1, patience=10,
verbose=False, threshold=1e-4, threshold_mode='rel',
cooldown=0, min_lr=0, eps=1e-8):
if factor >= 1.0:
raise ValueError('Factor should be < 1.0.')
self.factor = factor
if not isinstance(optimizer, Optimizer):
raise TypeError('{} is not an Optimizer'.format(
type(optimizer).__name__))
self.optimizer = optimizer
if isinstance(min_lr, list) or isinstance(min_lr, tuple):
if len(min_lr) != len(optimizer.param_groups):
raise ValueError("expected {} min_lrs, got {}".format(
len(optimizer.param_groups), len(min_lr)))
self.min_lrs = list(min_lr)
else:
self.min_lrs = [min_lr] * len(optimizer.param_groups)
self.patience = patience
self.verbose = verbose
self.cooldown = cooldown
self.cooldown_counter = 0
self.mode = mode
self.threshold = threshold
self.threshold_mode = threshold_mode
self.best = None
self.num_bad_epochs = None
self.mode_worse = None # the worse value for the chosen mode
self.eps = eps
self.last_epoch = -1
self._init_is_better(mode=mode, threshold=threshold,
threshold_mode=threshold_mode)
self._reset()
def _reset(self):
"""Resets num_bad_epochs counter and cooldown counter."""
self.best = self.mode_worse
self.cooldown_counter = 0
self.num_bad_epochs = 0
def step(self, metrics, epoch=None):
# convert `metrics` to float, in case it's a zero-dim Tensor
current = float(metrics)
if epoch is None:
epoch = self.last_epoch = self.last_epoch + 1
self.last_epoch = epoch
if self.is_better(current, self.best):
self.best = current
self.num_bad_epochs = 0
else:
self.num_bad_epochs += 1
if self.in_cooldown:
self.cooldown_counter -= 1
self.num_bad_epochs = 0 # ignore any bad epochs in cooldown
if self.num_bad_epochs > self.patience:
self._reduce_lr(epoch)
self.cooldown_counter = self.cooldown
self.num_bad_epochs = 0
def _reduce_lr(self, epoch):
for i, param_group in enumerate(self.optimizer.param_groups):
old_lr = float(param_group['lr'])
new_lr = max(old_lr * self.factor, self.min_lrs[i])
if old_lr - new_lr > self.eps:
param_group['lr'] = new_lr
if self.verbose:
print('Epoch {:5d}: reducing learning rate'
' of group {} to {:.4e}.'.format(epoch, i, new_lr))
@property
def in_cooldown(self):
return self.cooldown_counter > 0
def is_better(self, a, best):
if self.mode == 'min' and self.threshold_mode == 'rel':
rel_epsilon = 1. - self.threshold
return a < best * rel_epsilon
elif self.mode == 'min' and self.threshold_mode == 'abs':
return a < best - self.threshold
elif self.mode == 'max' and self.threshold_mode == 'rel':
rel_epsilon = self.threshold + 1.
return a > best * rel_epsilon
else: # mode == 'max' and epsilon_mode == 'abs':
return a > best + self.threshold
def _init_is_better(self, mode, threshold, threshold_mode):
if mode not in {'min', 'max'}:
raise ValueError('mode ' + mode + ' is unknown!')
if threshold_mode not in {'rel', 'abs'}:
raise ValueError('threshold mode ' + threshold_mode + ' is unknown!')
if mode == 'min':
self.mode_worse = inf
else: # mode == 'max':
self.mode_worse = -inf
self.mode = mode
self.threshold = threshold
self.threshold_mode = threshold_mode
def state_dict(self):
return {key: value for key, value in self.__dict__.items() if key != 'optimizer'}
def load_state_dict(self, state_dict):
self.__dict__.update(state_dict)
self._init_is_better(mode=self.mode, threshold=self.threshold, threshold_mode=self.threshold_mode)
[docs]class CyclicLR(_LRScheduler):
"""Sets the learning rate of each parameter group according to
cyclical learning rate policy (CLR). The policy cycles the learning
rate between two boundaries with a constant frequency, as detailed in
the paper `Cyclical Learning Rates for Training Neural Networks`_.
The distance between the two boundaries can be scaled on a per-iteration
or per-cycle basis.
Cyclical learning rate policy changes the learning rate after every batch.
`step` should be called after a batch has been used for training.
This class has three built-in policies, as put forth in the paper:
"triangular":
A basic triangular cycle w/ no amplitude scaling.
"triangular2":
A basic triangular cycle that scales initial amplitude by half each cycle.
"exp_range":
A cycle that scales initial amplitude by gamma**(cycle iterations) at each
cycle iteration.
This implementation was adapted from the github repo: `bckenstler/CLR`_
Args:
optimizer (Optimizer): Wrapped optimizer.
base_lr (float or list): Initial learning rate which is the
lower boundary in the cycle for each parameter group.
max_lr (float or list): Upper learning rate boundaries in the cycle
for each parameter group. Functionally,
it defines the cycle amplitude (max_lr - base_lr).
The lr at any cycle is the sum of base_lr
and some scaling of the amplitude; therefore
max_lr may not actually be reached depending on
scaling function.
step_size_up (int): Number of training iterations in the
increasing half of a cycle. Default: 2000
step_size_down (int): Number of training iterations in the
decreasing half of a cycle. If step_size_down is None,
it is set to step_size_up. Default: None
mode (str): One of {triangular, triangular2, exp_range}.
Values correspond to policies detailed above.
If scale_fn is not None, this argument is ignored.
Default: 'triangular'
gamma (float): Constant in 'exp_range' scaling function:
gamma**(cycle iterations)
Default: 1.0
scale_fn (function): Custom scaling policy defined by a single
argument lambda function, where
0 <= scale_fn(x) <= 1 for all x >= 0.
If specified, then 'mode' is ignored.
Default: None
scale_mode (str): {'cycle', 'iterations'}.
Defines whether scale_fn is evaluated on
cycle number or cycle iterations (training
iterations since start of cycle).
Default: 'cycle'
cycle_momentum (bool): If ``True``, momentum is cycled inversely
to learning rate between 'base_momentum' and 'max_momentum'.
Default: True
base_momentum (float or list): Lower momentum boundaries in the cycle
for each parameter group. Note that momentum is cycled inversely
to learning rate; at the peak of a cycle, momentum is
'base_momentum' and learning rate is 'max_lr'.
Default: 0.8
max_momentum (float or list): Upper momentum boundaries in the cycle
for each parameter group. Functionally,
it defines the cycle amplitude (max_momentum - base_momentum).
The momentum at any cycle is the difference of max_momentum
and some scaling of the amplitude; therefore
base_momentum may not actually be reached depending on
scaling function. Note that momentum is cycled inversely
to learning rate; at the start of a cycle, momentum is 'max_momentum'
and learning rate is 'base_lr'
Default: 0.9
last_epoch (int): The index of the last batch. This parameter is used when
resuming a training job. Since `step()` should be invoked after each
batch instead of after each epoch, this number represents the total
number of *batches* computed, not the total number of epochs computed.
When last_epoch=-1, the schedule is started from the beginning.
Default: -1
Example:
>>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
>>> scheduler = torch.optim.lr_scheduler.CyclicLR(optimizer, base_lr=0.01, max_lr=0.1)
>>> data_loader = torch.utils.data.DataLoader(...)
>>> for epoch in range(10):
>>> for batch in data_loader:
>>> train_batch(...)
>>> scheduler.step()
.. _Cyclical Learning Rates for Training Neural Networks: https://arxiv.org/abs/1506.01186
.. _bckenstler/CLR: https://github.com/bckenstler/CLR
"""
def __init__(self,
optimizer,
base_lr,
max_lr,
step_size_up=2000,
step_size_down=None,
mode='triangular',
gamma=1.,
scale_fn=None,
scale_mode='cycle',
cycle_momentum=True,
base_momentum=0.8,
max_momentum=0.9,
last_epoch=-1):
if not isinstance(optimizer, Optimizer):
raise TypeError('{} is not an Optimizer'.format(
type(optimizer).__name__))
self.optimizer = optimizer
base_lrs = self._format_param('base_lr', optimizer, base_lr)
if last_epoch == -1:
for lr, group in zip(base_lrs, optimizer.param_groups):
group['lr'] = lr
self.max_lrs = self._format_param('max_lr', optimizer, max_lr)
step_size_up = float(step_size_up)
step_size_down = float(step_size_down) if step_size_down is not None else step_size_up
self.total_size = step_size_up + step_size_down
self.step_ratio = step_size_up / self.total_size
if mode not in ['triangular', 'triangular2', 'exp_range'] \
and scale_fn is None:
raise ValueError('mode is invalid and scale_fn is None')
self.mode = mode
self.gamma = gamma
if scale_fn is None:
if self.mode == 'triangular':
self.scale_fn = self._triangular_scale_fn
self.scale_mode = 'cycle'
elif self.mode == 'triangular2':
self.scale_fn = self._triangular2_scale_fn
self.scale_mode = 'cycle'
elif self.mode == 'exp_range':
self.scale_fn = self._exp_range_scale_fn
self.scale_mode = 'iterations'
else:
self.scale_fn = scale_fn
self.scale_mode = scale_mode
self.cycle_momentum = cycle_momentum
if cycle_momentum:
if 'momentum' not in optimizer.defaults:
raise ValueError('optimizer must support momentum with `cycle_momentum` option enabled')
base_momentums = self._format_param('base_momentum', optimizer, base_momentum)
if last_epoch == -1:
for momentum, group in zip(base_momentums, optimizer.param_groups):
group['momentum'] = momentum
self.base_momentums = list(map(lambda group: group['momentum'], optimizer.param_groups))
self.max_momentums = self._format_param('max_momentum', optimizer, max_momentum)
super(CyclicLR, self).__init__(optimizer, last_epoch)
self.base_lrs = base_lrs
def _format_param(self, name, optimizer, param):
"""Return correctly formatted lr/momentum for each param group."""
if isinstance(param, (list, tuple)):
if len(param) != len(optimizer.param_groups):
raise ValueError("expected {} values for {}, got {}".format(
len(optimizer.param_groups), name, len(param)))
return param
else:
return [param] * len(optimizer.param_groups)
def _triangular_scale_fn(self, x):
return 1.
def _triangular2_scale_fn(self, x):
return 1 / (2. ** (x - 1))
def _exp_range_scale_fn(self, x):
return self.gamma**(x)
[docs] def get_lr(self):
"""Calculates the learning rate at batch index. This function treats
`self.last_epoch` as the last batch index.
If `self.cycle_momentum` is ``True``, this function has a side effect of
updating the optimizer's momentum.
"""
cycle = math.floor(1 + self.last_epoch / self.total_size)
x = 1. + self.last_epoch / self.total_size - cycle
if x <= self.step_ratio:
scale_factor = x / self.step_ratio
else:
scale_factor = (x - 1) / (self.step_ratio - 1)
lrs = []
for base_lr, max_lr in zip(self.base_lrs, self.max_lrs):
base_height = (max_lr - base_lr) * scale_factor
if self.scale_mode == 'cycle':
lr = base_lr + base_height * self.scale_fn(cycle)
else:
lr = base_lr + base_height * self.scale_fn(self.last_epoch)
lrs.append(lr)
if self.cycle_momentum:
momentums = []
for base_momentum, max_momentum in zip(self.base_momentums, self.max_momentums):
base_height = (max_momentum - base_momentum) * scale_factor
if self.scale_mode == 'cycle':
momentum = max_momentum - base_height * self.scale_fn(cycle)
else:
momentum = max_momentum - base_height * self.scale_fn(self.last_epoch)
momentums.append(momentum)
for param_group, momentum in zip(self.optimizer.param_groups, momentums):
param_group['momentum'] = momentum
return lrs
[docs]class CosineAnnealingWarmRestarts(_LRScheduler):
r"""Set the learning rate of each parameter group using a cosine annealing
schedule, where :math:`\eta_{max}` is set to the initial lr, :math:`T_{cur}`
is the number of epochs since the last restart and :math:`T_{i}` is the number
of epochs between two warm restarts in SGDR:
.. math::
\eta_t = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})(1 +
\cos(\frac{T_{cur}}{T_{i}}\pi))
When :math:`T_{cur}=T_{i}`, set :math:`\eta_t = \eta_{min}`.
When :math:`T_{cur}=0`(after restart), set :math:`\eta_t=\eta_{max}`.
It has been proposed in
`SGDR: Stochastic Gradient Descent with Warm Restarts`_.
Args:
optimizer (Optimizer): Wrapped optimizer.
T_0 (int): Number of iterations for the first restart.
T_mult (int, optional): A factor increases :math:`T_{i}` after a restart. Default: 1.
eta_min (float, optional): Minimum learning rate. Default: 0.
last_epoch (int, optional): The index of last epoch. Default: -1.
.. _SGDR\: Stochastic Gradient Descent with Warm Restarts:
https://arxiv.org/abs/1608.03983
"""
def __init__(self, optimizer, T_0, T_mult=1, eta_min=0, last_epoch=-1):
if T_0 <= 0 or not isinstance(T_0, int):
raise ValueError("Expected positive integer T_0, but got {}".format(T_0))
if T_mult < 1 or not isinstance(T_mult, int):
raise ValueError("Expected integer T_mult >= 1, but got {}".format(T_mult))
self.T_0 = T_0
self.T_i = T_0
self.T_mult = T_mult
self.eta_min = eta_min
super(CosineAnnealingWarmRestarts, self).__init__(optimizer, last_epoch)
self.T_cur = self.last_epoch
def get_lr(self):
return [self.eta_min + (base_lr - self.eta_min) * (1 + math.cos(math.pi * self.T_cur / self.T_i)) / 2
for base_lr in self.base_lrs]
[docs] def step(self, epoch=None):
"""Step could be called after every batch update
Example:
>>> scheduler = CosineAnnealingWarmRestarts(optimizer, T_0, T_mult)
>>> iters = len(dataloader)
>>> for epoch in range(20):
>>> for i, sample in enumerate(dataloader):
>>> inputs, labels = sample['inputs'], sample['labels']
>>> scheduler.step(epoch + i / iters)
>>> optimizer.zero_grad()
>>> outputs = net(inputs)
>>> loss = criterion(outputs, labels)
>>> loss.backward()
>>> optimizer.step()
This function can be called in an interleaved way.
Example:
>>> scheduler = CosineAnnealingWarmRestarts(optimizer, T_0, T_mult)
>>> for epoch in range(20):
>>> scheduler.step()
>>> scheduler.step(26)
>>> scheduler.step() # scheduler.step(27), instead of scheduler(20)
"""
if epoch is None:
epoch = self.last_epoch + 1
self.T_cur = self.T_cur + 1
if self.T_cur >= self.T_i:
self.T_cur = self.T_cur - self.T_i
self.T_i = self.T_i * self.T_mult
else:
if epoch < 0:
raise ValueError("Expected non-negative epoch, but got {}".format(epoch))
if epoch >= self.T_0:
if self.T_mult == 1:
self.T_cur = epoch % self.T_0
else:
n = int(math.log((epoch / self.T_0 * (self.T_mult - 1) + 1), self.T_mult))
self.T_cur = epoch - self.T_0 * (self.T_mult ** n - 1) / (self.T_mult - 1)
self.T_i = self.T_0 * self.T_mult ** (n)
else:
self.T_i = self.T_0
self.T_cur = epoch
self.last_epoch = math.floor(epoch)
for param_group, lr in zip(self.optimizer.param_groups, self.get_lr()):
param_group['lr'] = lr
[docs]class OneCycleLR(_LRScheduler):
r"""Sets the learning rate of each parameter group according to the
1cycle learning rate policy. The 1cycle policy anneals the learning
rate from an initial learning rate to some maximum learning rate and then
from that maximum learning rate to some minimum learning rate much lower
than the initial learning rate.
This policy was initially described in the paper `Super-Convergence:
Very Fast Training of Neural Networks Using Large Learning Rates`_.
The 1cycle learning rate policy changes the learning rate after every batch.
`step` should be called after a batch has been used for training.
This scheduler is not chainable.
This class has two built-in annealing strategies:
"cos":
Cosine annealing
"linear":
Linear annealing
Note also that the total number of steps in the cycle can be determined in one
of two ways (listed in order of precedence):
1) A value for total_steps is explicitly provided.
2) A number of epochs (epochs) and a number of steps per epoch
(steps_per_epoch) are provided.
In this case, the number of total steps is inferred by
total_steps = epochs * steps_per_epoch
You must either provide a value for total_steps or provide a value for both
epochs and steps_per_epoch.
Args:
optimizer (Optimizer): Wrapped optimizer.
max_lr (float or list): Upper learning rate boundaries in the cycle
for each parameter group.
total_steps (int): The total number of steps in the cycle. Note that
if a value is provided here, then it must be inferred by providing
a value for epochs and steps_per_epoch.
Default: None
epochs (int): The number of epochs to train for. This is used along
with steps_per_epoch in order to infer the total number of steps in the cycle
if a value for total_steps is not provided.
Default: None
steps_per_epoch (int): The number of steps per epoch to train for. This is
used along with epochs in order to infer the total number of steps in the
cycle if a value for total_steps is not provided.
Default: None
pct_start (float): The percentage of the cycle (in number of steps) spent
increasing the learning rate.
Default: 0.3
anneal_strategy (str): {'cos', 'linear'}
Specifies the annealing strategy.
Default: 'cos'
cycle_momentum (bool): If ``True``, momentum is cycled inversely
to learning rate between 'base_momentum' and 'max_momentum'.
Default: True
base_momentum (float or list): Lower momentum boundaries in the cycle
for each parameter group. Note that momentum is cycled inversely
to learning rate; at the peak of a cycle, momentum is
'base_momentum' and learning rate is 'max_lr'.
Default: 0.85
max_momentum (float or list): Upper momentum boundaries in the cycle
for each parameter group. Functionally,
it defines the cycle amplitude (max_momentum - base_momentum).
Note that momentum is cycled inversely
to learning rate; at the start of a cycle, momentum is 'max_momentum'
and learning rate is 'base_lr'
Default: 0.95
div_factor (float): Determines the initial learning rate via
initial_lr = max_lr/div_factor
Default: 25
final_div_factor (float): Determines the minimum learning rate via
min_lr = initial_lr/final_div_factor
Default: 1e4
last_epoch (int): The index of the last batch. This parameter is used when
resuming a training job. Since `step()` should be invoked after each
batch instead of after each epoch, this number represents the total
number of *batches* computed, not the total number of epochs computed.
When last_epoch=-1, the schedule is started from the beginning.
Default: -1
Example:
>>> data_loader = torch.utils.data.DataLoader(...)
>>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
>>> scheduler = torch.optim.lr_scheduler.OneCycleLR(optimizer, max_lr=0.01, steps_per_epoch=len(data_loader), epochs=10)
>>> for epoch in range(10):
>>> for batch in data_loader:
>>> train_batch(...)
>>> scheduler.step()
.. _Super-Convergence\: Very Fast Training of Neural Networks Using Large Learning Rates:
https://arxiv.org/abs/1708.07120
"""
def __init__(self,
optimizer,
max_lr,
total_steps=None,
epochs=None,
steps_per_epoch=None,
pct_start=0.3,
anneal_strategy='cos',
cycle_momentum=True,
base_momentum=0.85,
max_momentum=0.95,
div_factor=25.,
final_div_factor=1e4,
last_epoch=-1):
# Validate optimizer
if not isinstance(optimizer, Optimizer):
raise TypeError('{} is not an Optimizer'.format(
type(optimizer).__name__))
self.optimizer = optimizer
# Validate total_steps
if total_steps is None and epochs is None and steps_per_epoch is None:
raise ValueError("You must define either total_steps OR (epochs AND steps_per_epoch)")
elif total_steps is not None:
if total_steps <= 0 or not isinstance(total_steps, int):
raise ValueError("Expected non-negative integer total_steps, but got {}".format(total_steps))
self.total_steps = total_steps
else:
if epochs <= 0 or not isinstance(epochs, int):
raise ValueError("Expected non-negative integer epochs, but got {}".format(epochs))
if steps_per_epoch <= 0 or not isinstance(steps_per_epoch, int):
raise ValueError("Expected non-negative integer steps_per_epoch, but got {}".format(steps_per_epoch))
self.total_steps = epochs * steps_per_epoch
self.step_size_up = float(pct_start * self.total_steps) - 1
self.step_size_down = float(self.total_steps - self.step_size_up) - 1
# Validate pct_start
if pct_start < 0 or pct_start > 1 or not isinstance(pct_start, float):
raise ValueError("Expected float between 0 and 1 pct_start, but got {}".format(pct_start))
# Validate anneal_strategy
if anneal_strategy not in ['cos', 'linear']:
raise ValueError("anneal_strategy must by one of 'cos' or 'linear', instead got {}".format(anneal_strategy))
elif anneal_strategy == 'cos':
self.anneal_func = self._annealing_cos
elif anneal_strategy == 'linear':
self.anneal_func = self._annealing_linear
# Initialize learning rate variables
max_lrs = self._format_param('max_lr', self.optimizer, max_lr)
if last_epoch == -1:
for idx, group in enumerate(self.optimizer.param_groups):
group['lr'] = max_lrs[idx] / div_factor
group['max_lr'] = max_lrs[idx]
group['min_lr'] = group['lr'] / final_div_factor
# Initialize momentum variables
self.cycle_momentum = cycle_momentum
if self.cycle_momentum:
if 'momentum' not in self.optimizer.defaults and 'betas' not in self.optimizer.defaults:
raise ValueError('optimizer must support momentum with `cycle_momentum` option enabled')
self.use_beta1 = 'betas' in self.optimizer.defaults
max_momentums = self._format_param('max_momentum', optimizer, max_momentum)
base_momentums = self._format_param('base_momentum', optimizer, base_momentum)
if last_epoch == -1:
for m_momentum, b_momentum, group in zip(max_momentums, base_momentums, optimizer.param_groups):
if self.use_beta1:
_, beta2 = group['betas']
group['betas'] = (m_momentum, beta2)
else:
group['momentum'] = m_momentum
group['max_momentum'] = m_momentum
group['base_momentum'] = b_momentum
super(OneCycleLR, self).__init__(optimizer, last_epoch)
def _format_param(self, name, optimizer, param):
"""Return correctly formatted lr/momentum for each param group."""
if isinstance(param, (list, tuple)):
if len(param) != len(optimizer.param_groups):
raise ValueError("expected {} values for {}, got {}".format(
len(optimizer.param_groups), name, len(param)))
return param
else:
return [param] * len(optimizer.param_groups)
def _annealing_cos(self, start, end, pct):
"Cosine anneal from `start` to `end` as pct goes from 0.0 to 1.0."
cos_out = math.cos(math.pi * pct) + 1
return end + (start - end) / 2.0 * cos_out
def _annealing_linear(self, start, end, pct):
"Linearly anneal from `start` to `end` as pct goes from 0.0 to 1.0."
return (end - start) * pct + start
def get_lr(self):
lrs = []
step_num = self.last_epoch
if step_num > self.total_steps:
raise ValueError("Tried to step {} times. The specified number of total steps is {}"
.format(step_num + 1, self.total_steps))
for group in self.optimizer.param_groups:
if step_num <= self.step_size_up:
computed_lr = self.anneal_func(group['initial_lr'], group['max_lr'], step_num / self.step_size_up)
if self.cycle_momentum:
computed_momentum = self.anneal_func(group['max_momentum'], group['base_momentum'],
step_num / self.step_size_up)
else:
down_step_num = step_num - self.step_size_up
computed_lr = self.anneal_func(group['max_lr'], group['min_lr'], down_step_num / self.step_size_down)
if self.cycle_momentum:
computed_momentum = self.anneal_func(group['base_momentum'], group['max_momentum'],
down_step_num / self.step_size_down)
lrs.append(computed_lr)
if self.cycle_momentum:
if self.use_beta1:
_, beta2 = group['betas']
group['betas'] = (computed_momentum, beta2)
else:
group['momentum'] = computed_momentum
return lrs
