曲阜师范大学学报（自然科学版）2024，Vol.50Issue(4)：1-12,12.DOI:10.3969/j.issn.1001-5337.2024.4.001
求解一类随机变分不等式问题的带方差缩减的近端镜像滑动算法
A variance reduced mirror-prox sliding method for solving a class of stochastic monotone variational inequality
摘要
Abstract
In this paper,the authors consider new algorithm for solving a class of structured stochastic monotone variational inequality(SMVI),which is widely used in fields such as statistics,machine learning,and artificial intelligence.Specifically,the SMVI problem involves the sum of a gradient operator whose exact information is known and a monotone operator whose information is estimated by random samples,which makes the algorithm to solve the problem uncertain.The stochastic mirror-prox sliding algorithm is an effective algorithm to solve the SMVI problem,but the stochastic perturbation introduced by random information undermines the optimal computational complexity of monotone operator.Based on SMPS,in this paper,we use variance reduction technique for random monotone operators and propose a new algo-rithm,called variance reduced stochastic mirror-prox sliding algorithm(VRSMPS).In addition,under the general hypothesis of bounded variance,we prove that compared with SMPS,using VRSMPS to solve SMVI can obtain the optimal computational complexity of gradient operator O(√L/ε)and reduce the com-putational complexity of monotone operator from O(√L/ε+M/ε+σ2/ε2)to O(√L/ε+√(α+M2)2/Lε3).关键词
随机变分不等式/近端镜像滑动算法/方差缩减/计算复杂度Key words
stochastic variational inequality/mirror-prox sliding methods/variance reduction/computa-tional complexity分类
数理科学引用本文复制引用
王子玲,王丽平..求解一类随机变分不等式问题的带方差缩减的近端镜像滑动算法[J].曲阜师范大学学报（自然科学版）,2024,50(4):1-12,12.基金项目
国家自然科学基金(11971231,12111530001). （11971231,12111530001）
