def get_polynomial_decay_schedule_with_warmup(
        optimizer, num_warmup_steps, num_training_steps, lr_end=1e-7, power=1.0, last_epoch=-1
):
    """
    Create a schedule with a learning rate that decreases as a polynomial decay from the initial lr set in the
    optimizer to end lr defined by `lr_end`, after a warmup period during which it increases linearly from 0 to the
    initial lr set in the optimizer.

    Args:
        optimizer (:class:`~torch.optim.Optimizer`):
            The optimizer for which to schedule the learning rate.
        num_warmup_steps (:obj:`int`):
            The number of steps for the warmup phase.
        num_training_steps (:obj:`int`):
            The total number of training steps.
        lr_end (:obj:`float`, `optional`, defaults to 1e-7):
            The end LR.
        power (:obj:`float`, `optional`, defaults to 1.0):
            Power factor.
        last_epoch (:obj:`int`, `optional`, defaults to -1):
            The index of the last epoch when resuming training.

    Note: `power` defaults to 1.0 as in the fairseq implementation, which in turn is based on the original BERT
    implementation at
    https://github.com/google-research/bert/blob/f39e881b169b9d53bea03d2d341b31707a6c052b/optimization.py#L37

    Return:
        :obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.

    """

    lr_init = optimizer.defaults["lr"]
    if lr_init <= lr_end:
        raise ValueError(f"lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})")

    def lr_lambda(current_step: int):
        if current_step < num_warmup_steps:
            return float(current_step) / float(max(1, num_warmup_steps))
        elif current_step > num_training_steps:
            return lr_end / lr_init  # as LambdaLR multiplies by lr_init
        else:
            lr_range = lr_init - lr_end
            decay_steps = num_training_steps - num_warmup_steps
            pct_remaining = 1 - (current_step - num_warmup_steps) / decay_steps
            decay = lr_range * pct_remaining ** power + lr_end
            return decay / lr_init  # as LambdaLR multiplies by lr_init

    return LambdaLR(optimizer, lr_lambda, last_epoch)
Create a schedule with a learning rate that decreases as a polynomial decay from the initial lr set in the
optimizer to end lr defined by `lr_end`, after a warmup period during which it increases linearly from 0 to the
initial lr set in the optimizer.

Args:
optimizer (:class:`~torch.optim.Optimizer`):
The optimizer for which to schedule the learning rate.
num_warmup_steps (:obj:`int`):
The number of steps for the warmup phase.
num_training_steps (:obj:`int`):
The total number of training steps.
lr_end (:obj:`float`, `optional`, defaults to 1e-7):
The end LR.
power (:obj:`float`, `optional`, defaults to 1.0):
Power factor.
last_epoch (:obj:`int`, `optional`, defaults to -1):
The index of the last epoch when resuming training.

Note: `power` defaults to 1.0 as in the fairseq implementation, which in turn is based on the original BERT
implementation at
https://github.com/google-research/bert/blob/f39e881b169b9d53bea03d2d341b31707a6c052b/optimization.py#L37

Return:
:obj:`torch.optim.lr_scheduler.LambdaLR` with the appropriate schedule.
towhee/trainer/optimization/optimization.py