Large-Step Last-Iterate Convergence of Random-Reshuffling Stochastic Gradient Descent

Abstract:Random reshuffling stochastic gradient descent (RR-SGD) is widely used for finite-sum optimization in machine learning. For convex $L$-smooth components, recent work establishes convergence guarantees for an averaged iterate with component stepsizes as large as order $1/L$. However, the final iterate is a natural output in practice, and existing last-iterate guarantees in this setting require stepsizes that scale inversely with the number of components $n$. We establish an expected objective-gap bound for the last iterate of standard RR-SGD on unconstrained problems with a constant component stepsize satisfying $0<\eta\lesssim 1/(L(1 + \log(nK)))$, where $K$ is the number of epochs. By retaining the sampling bias at random comparison points, we remove the explicit $1/n$ factor from the stepsize restriction. Combined with existing small-step bounds, our result matches the corresponding averaged-iterate convergence rate up to logarithmic factors.

Optimization and Control (math.OC); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2610.19444 [math.OC]

(or arXiv:2610.19444v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2610.19444 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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