Mathematical Programming

, Volume 167, Issue 2, pp 235–292 | Cite as

Data-driven robust optimization

  • Dimitris Bertsimas
  • Vishal GuptaEmail author
  • Nathan Kallus
Full Length Paper Series A


The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee whenever the constraints and objective function are concave in the uncertainty. We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queueing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data are available.


Robust optimization Data-driven optimization Chance-constraints Hypothesis testing 

Mathematics Subject Classification

80M50 (Optimization: Operations research, mathematical programming) 62H15 (Multivariate Analysis: Hypothesis Testing) 



We would like to thank the area editor, associate editor and two anonymous reviewers for their helpful comments on an earlier draft of this manuscript. Part of this work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374.


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Copyright information

© Springer-Verlag Berlin Heidelberg 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 EngineeringCornell University and Cornell TechNew YorkUSA

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