A Second look at Exponential and Cosine Step Sizes: Simplicity, Adaptivity, and Performance

Xiaoyu Li, Zhenxun Zhuang, Francesco Orabona

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for tuning the step sizes have been proposed, ranging from coordinate-wise approaches (a.k.a. “adaptive” step sizes) to sophisticated heuristics to change the step size in each iteration. In this paper, we study two step size schedules whose power has been repeatedly confirmed in practice: the exponential and the cosine step sizes. For the first time, we provide theoretical support for them proving convergence rates for smooth non-convex functions, with and without the Polyak-Łojasiewicz (PL) condition. Moreover, we show the surprising property that these two strategies are adaptive to the noise level in the stochastic gradients of PL functions. That is, contrary to polynomial step sizes, they achieve almost optimal performance without needing to know the noise level nor tuning their hyperparameters based on it. Finally, we conduct a fair and comprehensive empirical evaluation of real-world datasets with deep learning architectures. Results show that, even if only requiring at most two hyperparameters to tune, these two strategies best or match the performance of various finely-tuned state-of-the-art strategies.
Original languageEnglish (US)
Title of host publicationProceedings of Machine Learning Research
PublisherML Research Press
Pages6553-6564
Number of pages12
ISBN (Print)9781713845065
StatePublished - Jan 1 2021
Externally publishedYes

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