It is common in deep learning to warm up the learning rate $\eta$, often by a linear schedule between $\eta_{\text{init}} = 0$ and a predetermined target $\eta_{\text{trgt}}$. In this paper, we show through systematic experiments using SGD and Adam that the overwhelming benefit of warmup arises from allowing the network to tolerate larger $\eta_{\text{trgt}}$ by forcing the network to more well-conditioned areas of the loss landscape. The ability to handle larger $\eta_{\text{trgt}}$ makes hyperparameter tuning more robust while improving the final performance. We uncover different regimes of operation during the warmup period, depending on whether training starts off in a progressive sharpening or sharpness reduction phase, which in turn depends on the initialization and parameterization. Using these insights, we show how $\eta_{\text{init}}$ can be properly chosen by utilizing the loss catapult mechanism, which saves on the number of warmup steps, in some cases completely eliminating the need for warmup. We also suggest an initialization for the variance in Adam which provides benefits similar to warmup.

通过系统性实验证明，深度学习中热身起始学习率对于训练结果的显著好处在于使网络能够容纳更大的目标学习率，并将网络推向更好条件的损失函数区域，从而提高超参数调优的鲁棒性和最终性能，同时揭示了不同热身阶段的运行模式，根据初始化和参数化的不同，在一定情况下可以完全消除热身的需要，并建议Adam中方差的初始化方式以获得类似热身的好处。

为什么要热身学习率？机制及改进