Technical Note: Data-Driven Sample Average Approximation with Covariate Information

• 成果类型: Article; Early Access
• 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: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.0533
• 发表日期: 2025
• 关键词: models; optimization

摘要

We study optimization for data-driven decision making when we have observations of the uncertain parameters within an optimization model together with concurrent observations of covariates. The goal is to choose a decision that minimizes the expected cost conditioned on a new covariate observation. We investigate two data-driven frameworks that integrate a machine learning prediction model within a stochastic programming sample average approximation (SAA) for approximating the solution to this problem. One SAA framework is new and uses leave-one-out residuals for scenario generation. The frameworks we investigate are flexible and accommodate parametric, nonparametric, and semiparametric regression techniques. We derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal, and also derive finite sample guarantees. Computational experiments validate our theoretical results, demonstrate examples where our data-driven formulations have advantages over existing approaches (even if the prediction model is misspecified), and illustrate the benefits of our data-driven formulations in the limited data regime.