IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v63y2015i3p628-638.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2015.1374
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2015.1374?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Arnab Nilim & Laurent El Ghaoui, 2005. "Robust Control of Markov Decision Processes with Uncertain Transition Matrices," Operations Research, INFORMS, vol. 53(5), pages 780-798, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shie Mannor & Ofir Mebel & Huan Xu, 2016. "Robust MDPs with k -Rectangular Uncertainty," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1484-1509, November.
    2. Erick Delage & Shie Mannor, 2010. "Percentile Optimization for Markov Decision Processes with Parameter Uncertainty," Operations Research, INFORMS, vol. 58(1), pages 203-213, February.
    3. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    4. Michael Jong Kim & Andrew E.B. Lim, 2016. "Robust Multiarmed Bandit Problems," Management Science, INFORMS, vol. 62(1), pages 264-285, January.
    5. Andrew E. B. Lim & J. George Shanthikumar, 2007. "Relative Entropy, Exponential Utility, and Robust Dynamic Pricing," Operations Research, INFORMS, vol. 55(2), pages 198-214, April.
    6. Erim Kardeş & Fernando Ordóñez & Randolph W. Hall, 2011. "Discounted Robust Stochastic Games and an Application to Queueing Control," Operations Research, INFORMS, vol. 59(2), pages 365-382, April.
    7. Li, Xingchen & Xu, Guangcheng & Wu, Jie & Xu, Chengzhen & Zhu, Qingyuan, 2024. "Evaluation of bank efficiency by considering the uncertainty of nonperforming loans," Omega, Elsevier, vol. 126(C).
    8. Christina Büsing & Sigrid Knust & Xuan Thanh Le, 2018. "Trade-off between robustness and cost for a storage loading problem: rule-based scenario generation," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 339-365, December.
    9. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    10. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    11. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    12. Chuong, T.D. & Jeyakumar, V., 2017. "Convergent hierarchy of SDP relaxations for a class of semi-infinite convex polynomial programs and applications," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 381-399.
    13. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    14. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    15. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    16. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    17. Evers, L. & Dollevoet, T.A.B. & Barros, A.I. & Monsuur, H., 2011. "Robust UAV Mission Planning," Econometric Institute Research Papers EI 2011-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Vaughn Gambeta & Roy Kwon, 2020. "Risk Return Trade-Off in Relaxed Risk Parity Portfolio Optimization," JRFM, MDPI, vol. 13(10), pages 1-28, October.
    19. J. Behnamian & Z. Gharabaghli, 2023. "Multi-objective outpatient scheduling in health centers considering resource constraints and service quality: a robust optimization approach," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-35, March.
    20. Mínguez, R. & García-Bertrand, R., 2016. "Robust transmission network expansion planning in energy systems: Improving computational performance," European Journal of Operational Research, Elsevier, vol. 248(1), pages 21-32.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:628-638. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.