A second look at exponential and cosine step sizes: simplicity, adaptivity, and performance
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Published version
Date
2021-07-18
DOI
Authors
Li, Xiaoyu
Zhuang, Zhenxun
Orabona, Francesco
Version
Published version
OA Version
Citation
X. Li, Z. Zhuang, F. Orabona. 2021. "A Second look at Exponential and Cosine Step Sizes: Simplicity, Adaptivity, and Performance." International Conference on Machine Learning, https://arxiv.org/abs/2002.05273
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.