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A Second look at Exponential and Cosine Step Sizes: Simplicity, Adaptivity, and Performance
Xiaoyu Li · Zhenxun Zhuang · Francesco Orabona

Thu Jul 22 08:40 PM -- 08:45 PM (PDT) @ None

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-\L{}ojasiewicz (PL) condition. Moreover, we show the surprising property that these two strategies are \emph{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.

Author Information

Xiaoyu Li (Boston University)
Zhenxun Zhuang (Boston University)
Francesco Orabona (Boston University)
Francesco Orabona

Francesco Orabona is an Assistant Professor at Boston University. His background covers both theoretical and practical aspects of machine learning and optimization. His current research interests lie in online learning, and more generally the problem of designing and analyzing adaptive and parameter-free learning algorithms. He received the PhD degree in Electrical Engineering at the University of Genoa in 2007. He is (co)author of more than 60 peer reviewed papers.

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