2024/03/11 by Konstantinos Emmanouilidis, Emmanouilidis, Konstantinos, René Víctor Valqui Vidal +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2403.07148
openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing convergence analyses of SEG focus on its with-replacement variants, while practical implementations of the method randomly reshuffle components and sequentially use them. Unlike the well-studied with-replacement variants, SEG with Random Reshuffling (SEG-RR) lacks established theoretical guarantees. In this work, we provide a convergence analysis of SEG-RR for three classes of VIPs: (i) strongly monotone, (ii) affine, and (iii) monotone. We derive conditions under which SEG-RR achieves a faster convergence rate than the uniform with-replacement sampling SEG. In the monotone setting, our analysis of SEG-RR guarantees convergence to an arbitrary accuracy without large batch sizes, a strong requirement needed in the classical with-replacement SEG. As a byproduct of our results, we provide convergence guarantees for Shuffle Once SEG (shuffles the data only at the beginning of the algorithm) and the Incremental Extragradient (does not shuffle the data). We supplement our analysis with experiments validating empirically the superior performance of SEG-RR over the classical with-replacement sampling SEG.