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Source code for torch.optim.lr_scheduler

import types
import math
from torch._six import inf
from functools import wraps
import warnings
import weakref
from collections import Counter
from bisect import bisect_right

from .optimizer import Optimizer


EPOCH_DEPRECATION_WARNING = (
    "The epoch parameter in `scheduler.step()` was not necessary and is being "
    "deprecated where possible. Please use `scheduler.step()` to step the "
    "scheduler. During the deprecation, if epoch is different from None, the "
    "closed form is used instead of the new chainable form, where available. "
    "Please open an issue if you are unable to replicate your use case: "
    "https://github.com/pytorch/pytorch/issues/new/choose."
)

SAVE_STATE_WARNING = "Please also save or load the state of the optimizer when saving or loading the scheduler."

class _LRScheduler(object):

    def __init__(self, optimizer, last_epoch=-1, verbose=False):

        # Attach optimizer
        if not isinstance(optimizer, Optimizer):
            raise TypeError('{} is not an Optimizer'.format(
                type(optimizer).__name__))
        self.optimizer = optimizer

        # Initialize epoch and base learning rates
        if last_epoch == -1:
            for group in optimizer.param_groups:
                group.setdefault('initial_lr', group['lr'])
        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 = [group['initial_lr'] for group in 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.verbose = verbose

        self.step()

    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_last_lr(self):
        """ Return last computed learning rate by current scheduler.
        """
        return self._last_lr

    def get_lr(self):
        # Compute learning rate using chainable form of the scheduler
        raise NotImplementedError

    def print_lr(self, is_verbose, group, lr, epoch=None):
        """Display the current learning rate.
        """
        if is_verbose:
            if epoch is None:
                print('Adjusting learning rate'
                      ' of group {} to {:.4e}.'.format(group, lr))
            else:
                print('Epoch {:5d}: adjusting learning rate'
                      ' of group {} to {:.4e}.'.format(epoch, group, lr))


    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

        class _enable_get_lr_call:

            def __init__(self, o):
                self.o = o

            def __enter__(self):
                self.o._get_lr_called_within_step = True
                return self

            def __exit__(self, type, value, traceback):
                self.o._get_lr_called_within_step = False

        with _enable_get_lr_call(self):
            if epoch is None:
                self.last_epoch += 1
                values = self.get_lr()
            else:
                warnings.warn(EPOCH_DEPRECATION_WARNING, UserWarning)
                self.last_epoch = epoch
                if hasattr(self, "_get_closed_form_lr"):
                    values = self._get_closed_form_lr()
                else:
                    values = self.get_lr()

        for i, data in enumerate(zip(self.optimizer.param_groups, values)):
            param_group, lr = data
            param_group['lr'] = lr
            self.print_lr(self.verbose, i, lr, epoch)

        self._last_lr = [group['lr'] for group in self.optimizer.param_groups]


[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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, verbose=False): 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) super(LambdaLR, self).__init__(optimizer, last_epoch, verbose)
[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. """ warnings.warn(SAVE_STATE_WARNING, UserWarning) 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`. """ warnings.warn(SAVE_STATE_WARNING, UserWarning) lr_lambdas = state_dict.pop('lr_lambdas') self.__dict__.update(state_dict) # Restore state_dict keys in order to prevent side effects # https://github.com/pytorch/pytorch/issues/32756 state_dict['lr_lambdas'] = lr_lambdas for idx, fn in enumerate(lr_lambdas): if fn is not None: self.lr_lambdas[idx].__dict__.update(fn)
def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.") return [base_lr * lmbda(self.last_epoch) for lmbda, base_lr in zip(self.lr_lambdas, self.base_lrs)]
[docs]class MultiplicativeLR(_LRScheduler): """Multiply the learning rate of each parameter group by the factor given in the specified 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. Example: >>> lmbda = lambda epoch: 0.95 >>> scheduler = MultiplicativeLR(optimizer, lr_lambda=lmbda) >>> for epoch in range(100): >>> train(...) >>> validate(...) >>> scheduler.step() """ def __init__(self, optimizer, lr_lambda, last_epoch=-1, verbose=False): 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) super(MultiplicativeLR, self).__init__(optimizer, last_epoch, verbose)
[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) # Restore state_dict keys in order to prevent side effects # https://github.com/pytorch/pytorch/issues/32756 state_dict['lr_lambdas'] = lr_lambdas for idx, fn in enumerate(lr_lambdas): if fn is not None: self.lr_lambdas[idx].__dict__.update(fn)
def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) if self.last_epoch > 0: return [group['lr'] * lmbda(self.last_epoch) for lmbda, group in zip(self.lr_lambdas, self.optimizer.param_groups)] else: return list(self.base_lrs)
[docs]class StepLR(_LRScheduler): """Decays the learning rate of each parameter group by gamma every step_size epochs. Notice that such decay can happen simultaneously with other changes to the learning rate from outside this scheduler. 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, verbose=False): self.step_size = step_size self.gamma = gamma super(StepLR, self).__init__(optimizer, last_epoch, verbose) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) if (self.last_epoch == 0) or (self.last_epoch % self.step_size != 0): return [group['lr'] for group in self.optimizer.param_groups] return [group['lr'] * self.gamma for group in self.optimizer.param_groups] def _get_closed_form_lr(self): return [base_lr * self.gamma ** (self.last_epoch // self.step_size) for base_lr in self.base_lrs]
[docs]class MultiStepLR(_LRScheduler): """Decays the learning rate of each parameter group by gamma once the number of epoch reaches one of the milestones. Notice that such decay can happen simultaneously with other changes to the learning rate from outside this scheduler. 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, verbose=False): self.milestones = Counter(milestones) self.gamma = gamma super(MultiStepLR, self).__init__(optimizer, last_epoch, verbose) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) if self.last_epoch not in self.milestones: return [group['lr'] for group in self.optimizer.param_groups] return [group['lr'] * self.gamma ** self.milestones[self.last_epoch] for group in self.optimizer.param_groups] def _get_closed_form_lr(self): milestones = list(sorted(self.milestones.elements())) return [base_lr * self.gamma ** bisect_right(milestones, self.last_epoch) for base_lr in self.base_lrs]
[docs]class ExponentialLR(_LRScheduler): """Decays the learning rate of each parameter group 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. """ def __init__(self, optimizer, gamma, last_epoch=-1, verbose=False): self.gamma = gamma super(ExponentialLR, self).__init__(optimizer, last_epoch, verbose) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) if self.last_epoch == 0: return self.base_lrs return [group['lr'] * self.gamma for group in self.optimizer.param_groups] def _get_closed_form_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:: \begin{aligned} \eta_t & = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})\left(1 + \cos\left(\frac{T_{cur}}{T_{max}}\pi\right)\right), & T_{cur} \neq (2k+1)T_{max}; \\ \eta_{t+1} & = \eta_{t} + \frac{1}{2}(\eta_{max} - \eta_{min}) \left(1 - \cos\left(\frac{1}{T_{max}}\pi\right)\right), & T_{cur} = (2k+1)T_{max}. \end{aligned} When last_epoch=-1, sets initial lr as lr. Notice that because the schedule is defined recursively, the learning rate can be simultaneously modified outside this scheduler by other operators. If the learning rate is set solely by this scheduler, the learning rate at each step becomes: .. math:: \eta_t = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})\left(1 + \cos\left(\frac{T_{cur}}{T_{max}}\pi\right)\right) 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. .. _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, verbose=False): self.T_max = T_max self.eta_min = eta_min super(CosineAnnealingLR, self).__init__(optimizer, last_epoch, verbose) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) if self.last_epoch == 0: return self.base_lrs elif (self.last_epoch - 1 - self.T_max) % (2 * self.T_max) == 0: return [group['lr'] + (base_lr - self.eta_min) * (1 - math.cos(math.pi / self.T_max)) / 2 for base_lr, group in zip(self.base_lrs, self.optimizer.param_groups)] return [(1 + math.cos(math.pi * self.last_epoch / self.T_max)) / (1 + math.cos(math.pi * (self.last_epoch - 1) / self.T_max)) * (group['lr'] - self.eta_min) + self.eta_min for group in self.optimizer.param_groups] def _get_closed_form_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. 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, threshold=1e-4, threshold_mode='rel', cooldown=0, min_lr=0, eps=1e-8, verbose=False): if factor >= 1.0: raise ValueError('Factor should be < 1.0.') self.factor = factor # Attach optimizer 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 = 0 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 + 1 else: warnings.warn(EPOCH_DEPRECATION_WARNING, UserWarning) 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 self._last_lr = [group['lr'] for group in self.optimizer.param_groups] 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): r"""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 without amplitude scaling. * "triangular2": A basic triangular cycle that scales initial amplitude by half each cycle. * "exp_range": A cycle that scales initial amplitude by :math:`\text{gamma}^{\text{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 verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, verbose=False): # Attach optimizer 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 = [group['momentum'] for group in optimizer.param_groups] self.max_momentums = self._format_param('max_momentum', optimizer, max_momentum) super(CyclicLR, self).__init__(optimizer, last_epoch, verbose) 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. """ if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) 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})\left(1 + \cos\left(\frac{T_{cur}}{T_{i}}\pi\right)\right) 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. verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. .. _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, verbose=False): 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, verbose) self.T_cur = self.last_epoch def get_lr(self): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) 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'] >>> optimizer.zero_grad() >>> outputs = net(inputs) >>> loss = criterion(outputs, labels) >>> loss.backward() >>> optimizer.step() >>> scheduler.step(epoch + i / iters) 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 and self.last_epoch < 0: epoch = 0 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) class _enable_get_lr_call: def __init__(self, o): self.o = o def __enter__(self): self.o._get_lr_called_within_step = True return self def __exit__(self, type, value, traceback): self.o._get_lr_called_within_step = False return self with _enable_get_lr_call(self): for i, data in enumerate(zip(self.optimizer.param_groups, self.get_lr())): param_group, lr = data param_group['lr'] = lr self.print_lr(self.verbose, i, lr, epoch) self._last_lr = [group['lr'] for group in self.optimizer.param_groups]
[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. Note also that the total number of steps in the cycle can be determined in one of two ways (listed in order of precedence): #. A value for total_steps is explicitly provided. #. 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. The default behaviour of this scheduler follows the fastai implementation of 1cycle, which claims that "unpublished work has shown even better results by using only two phases". To mimic the behaviour of the original paper instead, set ``three_phase=True``. 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 not 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: "cos" for cosine annealing, "linear" for linear annealing. 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 three_phase (bool): If ``True``, use a third phase of the schedule to annihilate the learning rate according to 'final_div_factor' instead of modifying the second phase (the first two phases will be symmetrical about the step indicated by 'pct_start'). 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 verbose (bool): If ``True``, prints a message to stdout for each update. Default: ``False``. 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, three_phase=False, last_epoch=-1, verbose=False): # 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 positive 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 positive integer epochs, but got {}".format(epochs)) if steps_per_epoch <= 0 or not isinstance(steps_per_epoch, int): raise ValueError("Expected positive integer steps_per_epoch, but got {}".format(steps_per_epoch)) self.total_steps = epochs * steps_per_epoch if three_phase: self._schedule_phases = [ { 'end_step': float(pct_start * self.total_steps) - 1, 'start_lr': 'initial_lr', 'end_lr': 'max_lr', 'start_momentum': 'max_momentum', 'end_momentum': 'base_momentum', }, { 'end_step': float(2 * pct_start * self.total_steps) - 2, 'start_lr': 'max_lr', 'end_lr': 'initial_lr', 'start_momentum': 'base_momentum', 'end_momentum': 'max_momentum', }, { 'end_step': self.total_steps - 1, 'start_lr': 'initial_lr', 'end_lr': 'min_lr', 'start_momentum': 'max_momentum', 'end_momentum': 'max_momentum', }, ] else: self._schedule_phases = [ { 'end_step': float(pct_start * self.total_steps) - 1, 'start_lr': 'initial_lr', 'end_lr': 'max_lr', 'start_momentum': 'max_momentum', 'end_momentum': 'base_momentum', }, { 'end_step': self.total_steps - 1, 'start_lr': 'max_lr', 'end_lr': 'min_lr', 'start_momentum': 'base_momentum', 'end_momentum': 'max_momentum', }, ] # 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['initial_lr'] = max_lrs[idx] / div_factor group['max_lr'] = max_lrs[idx] group['min_lr'] = group['initial_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, verbose) 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): if not self._get_lr_called_within_step: warnings.warn("To get the last learning rate computed by the scheduler, " "please use `get_last_lr()`.", UserWarning) 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: start_step = 0 for i, phase in enumerate(self._schedule_phases): end_step = phase['end_step'] if step_num <= end_step or i == len(self._schedule_phases) - 1: pct = (step_num - start_step) / (end_step - start_step) computed_lr = self.anneal_func(group[phase['start_lr']], group[phase['end_lr']], pct) if self.cycle_momentum: computed_momentum = self.anneal_func(group[phase['start_momentum']], group[phase['end_momentum']], pct) break start_step = phase['end_step'] 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

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