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Mathematical Programming

, Volume 171, Issue 1–2, pp 217–282 | Cite as

Robust sample average approximation

  • Dimitris Bertsimas
  • Vishal Gupta
  • Nathan Kallus
Full Length Paper Series A

Abstract

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA’s tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.

Keywords

Sample average approximation of stochastic optimization Data-driven optimization Goodness-of-fit testing Distributionally robust optimization Conic programming Inventory management Portfolio allocation 

Mathematics Subject Classification

90C15 62G10 90C47 90C34 90C25 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers and associate editor for their extremely helpful suggestions and very thorough review of the paper. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374.

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Copyright information

© Springer-Verlag GmbH Germany and Mathematical Optimization Society 2017

Authors and Affiliations

  1. 1.Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Marshall School of BusinessUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.School of Operations Research and Information Engineering and Cornell TechCornell UniversityNew YorkUSA

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