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

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

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arXiv · 2105.12342

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

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

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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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BibTeX RIS

Jun-ya Gotoh, Michael Jong Kim, Andrew E. B. Lim. 2021-05-26. A data-driven approach to beating SAA out-of-sample. https://arxiv.org/abs/2105.12342

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