Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming

• 成果类型: Article
• 署名作者: Zhang, Liwei; Zhang, Yule; Xiao, Xiantao; Wu, Jia
• 署名单位: Dalian University of Technology; Dalian Maritime University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1257
• 发表日期: 2023
• 页码: 177-193
• 关键词: composite optimization; algorithms

摘要

This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation proximal method of multipliers to solve this convex stochastic optimization problem. We analyze regrets of the proposed method for solving convex stochastic optimization problems. Under mild conditions, we show that this method exhibits sublinear regret for both objective reduction and constraint violation if parameters in the algorithm are properly chosen. Moreover, we investigate the high probability performance of the proposed method under the standard light-tail assumption.