Data-driven robust optimization

• Published in: Mathematical programming Vol. 167; no. 2; pp. 235 - 292
• Main Authors: Bertsimas, Dimitris, Gupta, Vishal, Kallus, Nathan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorics; Design optimization; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Nonlinear programming; Numerical Analysis; Operations research; Optimization techniques; Portfolio management; Queues; Statistical analysis; Theoretical; Uncertainty; Hypothesis testing; Robust optimization; Chance-constraints; 62H15 (Multivariate Analysis: Hypothesis Testing); 80M50 (Optimization: Operations research, mathematical programming); Data-driven optimization
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-017-1125-8

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.