DeepLearning - 余弦退火热重启学习率 CosineAnnealingWarmRestartsLR

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CosineAnnealingWarmRestartsLR，即 余弦退火热重启学习率，周期性修改学习率的下降和上升，间隔幅度逐渐增大，避免模型的性能抖动。其中核心参数：

• optimizer 的参数，lr 学习率，默认学习率是 lr * GPU 数量，例如 lr 设置成 0.00001，32卡实际是 0.00032。
• T_0，衰减的 global step 数，即单卡的运行次数，根据运行时间确定，例如 step 是 28.5 秒一次，(28.5 * 2000) / 3600 = 15.8 小时。
• T_mult，周期间隔，逐渐加大，例如 T_mult 是 2，则表示，第n次是 $T_0\ast T_{mult}^n$ 步。
• eta_min，从 LR 衰减的最小步数，可以设置成0。

源码：

optimizer = deepspeed.ops.adam.FusedAdam(self.model.parameters(), lr=learning_rate, eps=eps)
lr_scheduler = torch.optim.lr_scheduler.CosineAnnealingWarmRestarts(optimizer, T_0=lr_t_0, T_mult=2, eta_min=0, last_epoch=-1)
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LR 曲线如下：

源码：CosineAnnealingWarmRestarts

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(f"Expected positive integer T_0, but got {T_0}")
        if T_mult < 1 or not isinstance(T_mult, int):
            raise ValueError(f"Expected integer T_mult >= 1, but got {T_mult}")
        if not isinstance(eta_min, (float, int)):
            raise ValueError(f"Expected float or int eta_min, but got {eta_min} of type {type(eta_min)}")
        self.T_0 = T_0
        self.T_i = T_0
        self.T_mult = T_mult
        self.eta_min = eta_min
        self.T_cur = last_epoch
        super().__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)

        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:
            >>> # xdoctest: +SKIP("Undefined vars")
            >>> 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:
            >>> # xdoctest: +SKIP("Undefined vars")
            >>> 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(f"Expected non-negative epoch, but got {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]
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WandB 测试效果：

验证集效果也是周期更新：

参考：

• 知乎 - PyTorch中学习率调度器可视化介绍