def _check_inputs(learning_rate, decay_rate, total_step, step_per_epoch, decay_epoch, is_stair): validator.check_positive_int(total_step, 'total_step') validator.check_positive_int(step_per_epoch, 'step_per_epoch') validator.check_positive_int(decay_epoch, 'decay_epoch') validator.check_positive_float(learning_rate, 'learning_rate') validator.check_is_float(learning_rate, 'learning_rate') validator.check_positive_float(decay_rate, 'decay_rate') validator.check_is_float(decay_rate, 'decay_rate') validator.check_value_type('is_stair', is_stair, [bool])
def cosine_decay_lr(min_lr, max_lr, total_step, step_per_epoch, decay_epoch): r""" Calculate learning rate base on cosine decay function. For the i-th step, the formula of computing decayed_learning_rate[i] is: .. math:: decayed\_learning\_rate[i] = min\_learning\_rate + 0.5 * (max\_learning\_rate - min\_learning\_rate) * (1 + cos(\frac{current\_epoch}{decay\_epoch}\pi)) Where :math:`current\_epoch=floor(\frac{i}{step\_per\_epoch})`. Args: min_lr (float): The minimum value of learning rate. max_lr (float): The maximum value of learning rate. total_step (int): The total number of steps. step_per_epoch (int): The number of steps in per epoch. decay_epoch (int): A value used to calculate decayed learning rate. Returns: list[float]. The size of list is `total_step`. Examples: >>> min_lr = 0.01 >>> max_lr = 0.1 >>> total_step = 6 >>> step_per_epoch = 2 >>> decay_epoch = 2 >>> output = cosine_decay_lr(min_lr, max_lr, total_step, step_per_epoch, decay_epoch) >>> print(output) [0.1, 0.1, 0.05500000000000001, 0.05500000000000001, 0.01, 0.01] """ if not isinstance(min_lr, float): raise TypeError("min_lr must be float.") validator.check_non_negative_float(min_lr, "min_lr", None) validator.check_positive_float(max_lr, 'max_lr') validator.check_is_float(max_lr, 'max_lr') validator.check_positive_int(total_step, 'total_step') validator.check_positive_int(step_per_epoch, 'step_per_epoch') validator.check_positive_int(decay_epoch, 'decay_epoch') if min_lr >= max_lr: raise ValueError('`max_lr` should be greater than `min_lr`.') delta = 0.5 * (max_lr - min_lr) lr = [] for i in range(total_step): tmp_epoch = min(math.floor(i / step_per_epoch), decay_epoch) lr.append(min_lr + delta * (1 + math.cos(math.pi * tmp_epoch / decay_epoch))) return lr
def piecewise_constant_lr(milestone, learning_rates): r""" Get piecewise constant learning rate. Calculate learning rate by given `milestone` and `learning_rates`. Let the value of `milestone` be :math:`(M_1, M_2, ..., M_N)` and the value of `learning_rates` be :math:`(x_1, x_2, ..., x_N)`. N is the length of `milestone`. Let the output learning rate be `y`. .. math:: y[i] = x_t,\ for\ i \in [M_{t-1}, M_t) Args: milestone (Union[list[int], tuple[int]]): A list of milestone. This list is a monotone increasing list. Every element is a milestone step, and must be greater than 0. learning_rates (Union[list[float], tuple[float]]): A list of learning rates. Returns: list[float]. The size of list is :math:`M_N`. Examples: >>> milestone = [2, 5, 10] >>> learning_rates = [0.1, 0.05, 0.01] >>> output = piecewise_constant_lr(milestone, learning_rates) >>> print(output) [0.1, 0.1, 0.05, 0.05, 0.05, 0.01, 0.01, 0.01, 0.01, 0.01] """ validator.check_value_type('milestone', milestone, (tuple, list)) validator.check_value_type('learning_rates', learning_rates, (tuple, list)) if len(milestone) != len(learning_rates): raise ValueError( 'The size of `milestone` must be same with the size of `learning_rates`.' ) lr = [] last_item = 0 for i, item in enumerate(milestone): validator.check_positive_int(item, f'milestone[{i}]') validator.check_is_float(learning_rates[i], f'learning_rates[{i}]') if item < last_item: raise ValueError( f'The value of milestone[{i}] must be greater than milestone[{i - 1}]' ) lr += [learning_rates[i]] * (item - last_item) last_item = item return lr
def polynomial_decay_lr(learning_rate, end_learning_rate, total_step, step_per_epoch, decay_epoch, power, update_decay_epoch=False): r""" Calculate learning rate base on polynomial decay function. For the i-th step, the formula of computing decayed_learning_rate[i] is: .. math:: decayed\_learning\_rate[i] = (learning\_rate - end\_learning\_rate) * (1 - tmp\_epoch / tmp\_decay\_epoch)^{power} + end\_learning\_rate Where: .. math:: tmp\_epoch = min(current\_epoch, decay\_epoch) .. math:: current\_epoch=floor(\frac{i}{step\_per\_epoch}) .. math:: tmp\_decay\_epoch = decay\_epoch If `update_decay_epoch` is true, update the value of `tmp_decay_epoch` every epoch. The formula is: .. math:: tmp\_decay\_epoch = decay\_epoch * ceil(current\_epoch / decay\_epoch) Args: learning_rate (float): The initial value of learning rate. end_learning_rate (float): The end value of learning rate. total_step (int): The total number of steps. step_per_epoch (int): The number of steps in per epoch. decay_epoch (int): A value used to calculate decayed learning rate. power (float): A value used to calculate decayed learning rate. This parameter must be greater than 0. update_decay_epoch (bool): If true, update `decay_epoch`. Default: False. Returns: list[float]. The size of list is `total_step`. Examples: >>> learning_rate = 0.1 >>> end_learning_rate = 0.01 >>> total_step = 6 >>> step_per_epoch = 2 >>> decay_epoch = 2 >>> power = 0.5 >>> r = polynomial_decay_lr(learning_rate, end_learning_rate, total_step, step_per_epoch, decay_epoch, power) >>> print(r) [0.1, 0.1, 0.07363961030678928, 0.07363961030678928, 0.01, 0.01] """ validator.check_positive_float(learning_rate, 'learning_rate') validator.check_is_float(learning_rate, 'learning_rate') if not isinstance(end_learning_rate, float): raise TypeError("end_learning_rate must be float.") validator.check_non_negative_float(end_learning_rate, "end_learning_rate", None) validator.check_positive_float(power, 'power') validator.check_is_float(power, 'power') validator.check_positive_int(total_step, 'total_step') validator.check_positive_int(step_per_epoch, 'step_per_epoch') validator.check_positive_int(decay_epoch, 'decay_epoch') validator.check_value_type('update_decay_epoch', update_decay_epoch, [bool]) origin_decay_epoch = decay_epoch function = lambda x, y: (x, min(x, y)) if update_decay_epoch: function = lambda x, y: (origin_decay_epoch * max( math.ceil(y / origin_decay_epoch), 1), y) lr = [] delta = learning_rate - end_learning_rate for i in range(total_step): current_epoch = math.floor(i / step_per_epoch) decay_epoch, tmp_epoch = function(decay_epoch, current_epoch) lr.append(delta * (1 - tmp_epoch / decay_epoch)**power + end_learning_rate) return lr