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Oracle-Based Robust Optimization via Online Learning

Author

Listed:
  • Aharon Ben-Tal

    (Department of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 3200003 Israel; and Center for Economic Research, Tilburg University, 5037 AB Tilburg, Netherlands)

  • Elad Hazan

    (Department of Computer Science, Princeton University, Princeton, New Jersey 08544)

  • Tomer Koren

    (Department of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 3200003 Israel)

  • Shie Mannor

    (Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa 3200003 Israel)

Abstract

Robust optimization is a common optimization framework under uncertainty when problem parameters are unknown, but it is known that they belong to some given uncertainty set. In the robust optimization framework, a min-max problem is solved wherein a solution is evaluated according to its performance on the worst possible realization of the parameters. In many cases, a straightforward solution to a robust optimization problem of a certain type requires solving an optimization problem of a more complicated type, which might be NP-hard in some cases. For example, solving a robust conic quadratic program, such as those arising in a robust support vector machine (SVM) with an ellipsoidal uncertainty set, leads in general to a semidefinite program. In this paper, we develop a method for approximately solving a robust optimization problem using tools from online convex optimization, where at every stage a standard (nonrobust) optimization program is solved. Our algorithms find an approximate robust solution using a number of calls to an oracle that solves the original (nonrobust) problem that is inversely proportional to the square of the target accuracy.

Suggested Citation

  • Aharon Ben-Tal & Elad Hazan & Tomer Koren & Shie Mannor, 2015. "Oracle-Based Robust Optimization via Online Learning," Operations Research, INFORMS, vol. 63(3), pages 628-638, June.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:628-638
    DOI: 10.1287/opre.2015.1374
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    References listed on IDEAS

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    1. Serge A. Plotkin & David B. Shmoys & Éva Tardos, 1995. "Fast Approximation Algorithms for Fractional Packing and Covering Problems," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 257-301, May.
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    Cited by:

    1. Denizalp Goktas & Amy Greenwald, 2022. "Gradient Descent Ascent in Min-Max Stackelberg Games," Papers 2208.09690, arXiv.org.
    2. Ho-Nguyen, Nam, 2020. "Two-Stage Stochastic and Robust Optimization for Non-Adaptive Group Testing," Working Papers BAWP-2020-04, University of Sydney Business School, Discipline of Business Analytics.
    3. Juan S. Borrero & Leonardo Lozano, 2021. "Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1570-1589, October.
    4. Mehdi Ansari & Juan S. Borrero & Leonardo Lozano, 2023. "Robust Minimum-Cost Flow Problems Under Multiple Ripple Effect Disruptions," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 83-103, January.
    5. Yue Zhou-Kangas & Kaisa Miettinen, 2019. "Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 391-413, June.

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