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Source code for torch.optim.lr_scheduler

import types
import math
from torch._six import inf
from collections import Counter
from functools import partial

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'])
        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.step(last_epoch + 1)
        self.last_epoch = 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):
        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): >>> scheduler.step() >>> train(...) >>> validate(...) """ 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): """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. 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): >>> scheduler.step() >>> train(...) >>> validate(...) """ 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): 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]
[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. 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): >>> scheduler.step() >>> train(...) >>> validate(...) """ def __init__(self, optimizer, milestones, gamma=0.1, last_epoch=-1): self.milestones = Counter(milestones) self.gamma = gamma super(MultiStepLR, self).__init__(optimizer, last_epoch) def get_lr(self): 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]
[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. """ def __init__(self, optimizer, gamma, last_epoch=-1): self.gamma = gamma super(ExponentialLR, self).__init__(optimizer, last_epoch) def get_lr(self): if self.last_epoch == 0: return self.base_lrs return [group['lr'] * self.gamma for group in self.optimizer.param_groups]
[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+1} = \eta_{min} + (\eta_t - \eta_{min})\frac{1 + \cos(\frac{T_{cur+1}}{T_{max}}\pi)}{1 + \cos(\frac{T_{cur}}{T_{max}}\pi)} 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})(1 + \cos(\frac{T_{cur}}{T_{max}}\pi)) 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): if self.last_epoch == 0: return self.base_lrs 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]
[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.is_better = None 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 _cmp(self, mode, threshold_mode, threshold, a, best): if mode == 'min' and threshold_mode == 'rel': rel_epsilon = 1. - threshold return a < best * rel_epsilon elif mode == 'min' and threshold_mode == 'abs': return a < best - threshold elif mode == 'max' and threshold_mode == 'rel': rel_epsilon = threshold + 1. return a > best * rel_epsilon else: # mode == 'max' and epsilon_mode == 'abs': return a > best + 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.is_better = partial(self._cmp, mode, threshold_mode, threshold) def state_dict(self): return {key: value for key, value in self.__dict__.items() if key not in {'optimizer', 'is_better'}} 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): Initial momentum which is the lower boundary in the cycle for each parameter group. 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. 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.CyclicLR(optimizer) >>> 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) 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

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