Residuals-based distributionally robust optimization with covariate information

• 成果类型: Article
• 署名作者: Kannan, Rohit; Bayraksan, Guezin; Luedtke, James R.
• 署名单位: Virginia Polytechnic Institute & State University; University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-02014-7
• 发表日期: 2024
• 页码: 369-425
• 关键词: linear-programs; reformulations; CONVERGENCE

摘要

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.