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arXiv · 2106.09687

Super-Acceleration with Cyclical Step-sizes

Baptiste Goujaud·Damien Scieur·Aymeric Dieuleveut·Adrien Taylor·Fabian Pedregosa
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Abstract

We develop a convergence-rate analysis of momentum with cyclical step-sizes. We show that under some assumption on the spectral gap of Hessians in machine learning, cyclical step-sizes are provably faster than constant step-sizes. More precisely, we develop a convergence rate analysis for quadratic objectives that provides optimal parameters and shows that cyclical learning rates can improve upon traditional lower complexity bounds. We further propose a systematic approach to design optimal first order methods for quadratic minimization with a given spectral structure. Finally, we provide a local convergence rate analysis beyond quadratic minimization for the proposed methods and illustrate our findings through benchmarks on least squares and logistic regression problems.

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Baptiste Goujaud, Damien Scieur, Aymeric Dieuleveut, Adrien Taylor, Fabian Pedregosa. 2021-06-17. Super-Acceleration with Cyclical Step-sizes. https://arxiv.org/abs/2106.09687

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