A data-driven approach to beating SAA out-of-sample
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.
Cite
@article{arxiv.2105.12342,
title = {A data-driven approach to beating SAA out-of-sample},
author = {Jun-ya Gotoh and Michael Jong Kim and Andrew E. B. Lim},
journal= {arXiv preprint arXiv:2105.12342},
year = {2023}
}
Comments
25 pages, 2 page bibliography, 2 Figures, 12 page Appendix