An Accelerated Stochastic Mirror Descent Method

作     者：Bo-Ou Jiang Ya-Xiang Yuan 

作者机构：LSECICMSECAMSSChinese Academy of SciencesBeijing100190China Department of MathematicsUniversity of Chinese Academy of SciencesBeijing100049China 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2024年第12卷第3期

页      面：549-571页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China, NSFC, (1228201) National Natural Science Foundation of China, NSFC 

主　　题：Large-scale optimization Variance reduction Mirror descent Acceleration Independent sampling Importance sampling 

摘      要：Driven by large-scale optimization problems arising from machine learning,the development of stochastic optimization methods has witnessed a huge *** types of methods have been developed based on vanilla stochastic gradient descent ***,for most algorithms,convergence rate in stochastic setting cannot simply match that in deterministic *** understanding the gap between deterministic and stochastic optimization is the main goal of this ***,we are interested in Nesterov acceleration of gradient-based *** our study,we focus on acceleration of stochastic mirror descent method with implicit regularization *** that the problem objective is smooth and convex or strongly convex,our analysis prescribes the method parameters which ensure fast convergence of the estimation error and satisfied numerical performance.