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Technical Note—A Data-Driven Approach to Beating SAA Out of Sample

Author

Listed:
  • Jun-ya Gotoh

    (Department of Data Science for Business Innovation, Chuo University, Tokyo 112-8551, Japan)

  • Michael Jong Kim

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

  • Andrew E. B. Lim

    (Department of Analytics and Operations, Department of Finance, and Institute for Operations Research and Analytics, National University of Singapore, Singapore 119245)

Abstract

Whereas solutions of distributionally robust optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the sample average approximation (SAA), there is no guarantee. In this paper, we introduce a class of distributionally optimistic optimization (DOO) models and show that it is always possible to “beat” SAA out-of-sample if we consider not just worst case (DRO) models but also best case (DOO) ones. We also show, however, that this comes at a cost: optimistic solutions are more sensitive to model error than either worst case or SAA optimizers and, hence, are less robust, and calibrating the worst or best case model to outperform SAA may be difficult when data are limited.

Suggested Citation

  • Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2025. "Technical Note—A Data-Driven Approach to Beating SAA Out of Sample," Operations Research, INFORMS, vol. 73(2), pages 829-841, March.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:2:p:829-841
    DOI: 10.1287/opre.2021.0393
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    Keywords

    Optimization;

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