Super-Acceleration with Cyclical Step-sizes
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.
Cite
@article{arxiv.2106.09687,
title = {Super-Acceleration with Cyclical Step-sizes},
author = {Baptiste Goujaud and Damien Scieur and Aymeric Dieuleveut and Adrien Taylor and Fabian Pedregosa},
journal= {arXiv preprint arXiv:2106.09687},
year = {2022}
}