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A data-driven approach to beating SAA out-of-sample

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  • Jun-ya Gotoh
  • Michael Jong Kim
  • Andrew E. B. Lim

Abstract

While 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 is limited.

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  • Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2021. "A data-driven approach to beating SAA out-of-sample," Papers 2105.12342, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2105.12342
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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
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