Decision Making with Side Information: A Causal Transport Robust Approach

• 成果类型: Article
• 署名作者: Yang, Jincheng; Zhang, Luhao; Chen, Ningyuan; Gao, Rui; Hu, Ming
• 署名单位: Johns Hopkins University; University of Toronto; University Toronto Mississauga; University of Toronto; University of Texas System; University of Texas Austin
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0997
• 发表日期: 2026
• 关键词: affine policies; K-adaptability; optimization; ambiguity; PRODUCTS

摘要

We consider stochastic optimization with side information where, prior to decision making, covariate data are available to inform better decisions. To hedge against data uncertainty while capturing the information structure revealed from the conditional distribution of random problem parameters given the covariate values, we propose a distributionally robust formulation based on causal transport distance. We derive a dual reformulation for evaluating the worst-case expected cost and show that the worst-case distribution in a causal transport distance ball preserves the conditional information structure from the nominal distribution. When optimizing over affine decision rules, we identify cases in which the overall problem can be solved via convex programming. When optimizing over all (nonparametric) decision rules, we identify a new class of robust optimal decision rules when the cost function is convex with respect to a one-dimensional decision variable.