Papers › Super-Acceleration with Cyclical Step-sizes

Super-Acceleration with Cyclical Step-sizes

17 Jun 2021arXiv:2106.09687links table onlyarchive 2025-07-28

Baptiste Goujaud, Damien Scieur, Aymeric Dieuleveut, Adrien Taylor, Fabian Pedregosa

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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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