Technical Note—Data-Driven Sample Average Approximation with Covariate Information
Rohit Kannan, Güzin Bayraksan, James R. Luedtke
Operations Research · 2025 · Volume 73 · Issue 6
Abstract
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. Funding: This research was supported by the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract number DE-AC02-06CH11357. R. Kannan also gratefully acknowledges funding through the LANL/LDRD Program and the Center for Nonlinear Studies. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0533 .
Keywords
Optimization, data-driven stochastic programming, covariates, regression, sample average approximation, jackknife, large deviations
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