Why Warmup the Learning Rate? Underlying Mechanisms and Improvements

TL;DR

This paper investigates the mechanisms behind learning rate warmup in deep learning, revealing it enables training with larger learning rates by improving the loss landscape conditioning, and proposes methods to optimize warmup and initialization.

Contribution

It uncovers the underlying reasons for warmup's effectiveness, introduces regimes of training dynamics, and proposes strategies to reduce or eliminate warmup through better initialization.

Findings

Warmup allows larger learning rates by better conditioning the loss landscape.

Different training regimes depend on initialization and parameterization.

Proper initialization can reduce or eliminate the need for warmup.

Abstract

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.