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Learning-Based Robust Optimization: Procedures and Statistical Guarantees

Author

Listed:
  • L. Jeff Hong

    (School of Management and School of Data Science, Fudan University, Shanghai 200433, China)

  • Zhiyuan Huang

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

  • Henry Lam

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Robust optimization (RO) is a common approach to tractably obtain safeguarding 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.

Suggested Citation

  • L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:6:p:3447-3467
    DOI: 10.1287/mnsc.2020.3640
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    References listed on IDEAS

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