Using a one dimensional parabolic model of the full-batch loss to estimate learning rates during training

Maximus Mutschler, Kevin Alexander Laube, Andreas Zell

Keywords: Empirics based Optimization, Optimization, Line Search, SGD, Deep Learning

Abstract: A fundamental challenge in Deep Learning is to find optimal step sizes for stochastic gradient descent automatically. In traditional optimization, line searches are a commonly used method to determine step sizes. One problem in Deep Learning is that finding appropriate step sizes on the full-batch loss is unfeasibly expensive. Therefore, classical line search approaches, designed for losses without inherent noise, are usually not applicable. Recent empirical findings suggest that the full-batch loss behaves locally parabolically in the direction of noisy update step directions. Furthermore, the trend of the optimal update step size changes slowly. By exploiting these findings, this work introduces a line-search method that approximates the full-batch loss with a parabola estimated over several mini-batches. Learning rates are derived from such parabolas during training. In the experiments conducted, our approach mostly outperforms SGD tuned with a piece-wise constant learning rate schedule and other line search approaches for Deep Learning across models, datasets, and batch sizes on validation and test accuracy.

One-sentence Summary: Using a one dimensional parabolic model of the full-batch loss to estimate learning rates during training.