Data-driven robust optimization
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 flexibl...
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| Published in | Mathematical programming Vol. 167; no. 2; pp. 235 - 292 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0025-5610 1436-4646 |
| DOI | 10.1007/s10107-017-1125-8 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bertsimas, Dimitris Kallus, Nathan Gupta, Vishal |
| Author_xml | – sequence: 1 givenname: Dimitris orcidid: 0000-0002-1985-1003 surname: Bertsimas fullname: Bertsimas, Dimitris organization: Sloan School of Management, Massachusetts Institute of Technology – sequence: 2 givenname: Vishal surname: Gupta fullname: Gupta, Vishal email: guptavis@usc.edu organization: Marshall School of Business, University of Southern California – sequence: 3 givenname: Nathan surname: Kallus fullname: Kallus, Nathan organization: School of Operations Research and Information Engineering, Cornell University and Cornell Tech |
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| ContentType | Journal Article |
| Copyright | Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017 Mathematical Programming is a copyright of Springer, (2017). All Rights Reserved. |
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| Keywords | Hypothesis testing Robust optimization Chance-constraints 62H15 (Multivariate Analysis: Hypothesis Testing) 80M50 (Optimization: Operations research, mathematical programming) Data-driven optimization |
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| SubjectTerms | 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 |
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| Title | Data-driven robust optimization |
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