Stability and Sample-Based Approximations of Composite Stochastic Optimization Problems

• 成果类型: Article
• 署名作者: Dentcheva, Darinka; Lin, Yang; Penev, Spiridon
• 署名单位: Stevens Institute of Technology; University of New South Wales Sydney; University of New South Wales Sydney
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2308
• 发表日期: 2023
• 页码: 1871-1888
• 关键词: CENTRAL LIMIT-THEOREMS; uniform consistency; density; CONVERGENCE; PROGRAMS; weak

摘要

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals that are subjected to multiple measure perturbations. Our main focus is the asymptotic behavior of data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions. We analyze the properties of the new estimators and we establish strong law of large numbers, consistency, and bias reduction potential under fairly general assumptions. Our results are germane to risk-averse optimization and to data science in general.