A single cut proximal bundle method for stochastic convex composite optimization

• 成果类型: Article
• 署名作者: Liang, Jiaming; Guigues, Vincent; Monteiro, Renato D. C.
• 署名单位: University of Rochester; University of Rochester; Getulio Vargas Foundation; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-02035-2
• 发表日期: 2024
• 页码: 173-208
• 关键词: average approximation method; CONVERGENCE; algorithm; PROGRAMS

摘要

This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it. Complexity guarantees are established for them without requiring knowledge of parameters associated with the problem instance. Moreover, it is shown that they have optimal complexity when these problem parameters are known. To the best of our knowledge, this is the first proximal bundle method for stochastic programming able to deal with continuous distributions. Finally, we present computational results showing that SCPB substantially outperforms the robust stochastic approximation method in all instances considered.