Solving Nonsmooth and Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization

• 成果类型: Article; Early Access
• 署名作者: Liu, Junyi; Cui, Ying; Pang, Jong-Shi
• 署名单位: Tsinghua University; University of Minnesota System; University of Minnesota Twin Cities; University of Southern California
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1247
• 发表日期: 2022
• 关键词: sample average approximation; Value-at-risk; large numbers; buffered probability; Failure probability; cvar optimization; DECOMPOSITION; LAW

摘要

This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex programming-based sampling algorithm and establish its subsequential convergence. We describe stationary properties of the limit points for several classes of the compound SP. We further discuss probabilistic stopping rules based on the computable error bound for the algorithm. We present several risk measure minimization problems that can be formulated as such a compound stochastic program; these include generalized deviation optimization problems based on the optimized certainty equivalent and buffered probability of exceedance (bPOE), a distributionally robust bPOE optimization problem, and a multi class classification problem employing the cost-sensitive error criteria with bPOE.