A multi-factor (or piecewise constant) learning rate scheduler decreases the learning rate by a specific factor at predefined milestone epochs. While modern frameworks offer built-in solutions—such as torch.optim.lr_scheduler.MultiStepLR in PyTorch and lr_scheduler.MultiFactorScheduler in MXNet—this strategy can also be implemented from scratch. The following Python code demonstrates a custom scheduler that multiplies the base learning rate by a given factor whenever the current epoch is found in the predefined set of milestone steps:

class MultiFactorScheduler:
    def __init__(self, step, factor, base_lr):
        self.step = step
        self.factor = factor
        self.base_lr = base_lr

    def __call__(self, epoch):
        if epoch in self.step:
            self.base_lr = self.base_lr * self.factor
            return self.base_lr
        else:
            return self.base_lr