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

Jun-ya Gotoh (), Michael Jong Kim () and Andrew E. B. Lim ()
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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

Operations Research, 2025, vol. 73, issue 2, 829-841

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.

Keywords: Optimization; distributionally optimistic optimization; distributionally robust optimization; sample average approximation; data-driven optimization; model uncertainty; worst case sensitivity; out-of-sample performance (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:2:p:829-841

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