Learning-Based Robust Optimization: Procedures and Statistical Guarantees

• 成果类型: Article
• 署名作者: Hong, L. Jeff; Huang, Zhiyuan; Lam, Henry
• 署名单位: Fudan University; Fudan University; University of Michigan System; University of Michigan; Columbia University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2020.3640
• 发表日期: 2021
• 页码: 3447-3467
• 关键词: Robust Optimization; chance constraint; prediction set learning; quantile estimation

摘要

Robust optimization (RO) is a common approach to tractably obtain safe-guarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO based on learning a prediction set using (combinations of) geometric shapes that are compatible with established RO tools and on a simple data-splitting validation step that achieves finite-sample nonparametric statistical guarantees on feasibility. We demonstrate how our required sample size to achieve feasibility at a given confidence level is independent of the dimensions of both the decision space and the probability space governing the stochasticity, and we discuss some approaches to improve the objective performances while maintaining these dimension-free statistical feasibility guarantees.