IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v49y2024i4p2468-2491.html
   My bibliography  Save this article

Linear Program-Based Policies for Restless Bandits: Necessary and Sufficient Conditions for (Exponentially Fast) Asymptotic Optimality

Author

Listed:
  • Nicolas Gast

    (University of Grenoble Alpes, Institut national de recherche en informatique et en automatique, Centre national de la recherche scientifique, Grenoble Institut national polytechnique, Laboratoire d’informatique de Grenoble, 38000 Grenoble, France)

  • Bruno Gaujal

    (University of Grenoble Alpes, Institut national de recherche en informatique et en automatique, Centre national de la recherche scientifique, Grenoble Institut national polytechnique, Laboratoire d’informatique de Grenoble, 38000 Grenoble, France)

  • Chen Yan

    (STATIFY, Institut national de recherche en informatique et en automatique, 38334 Saint Ismier, France; Biostatistics and Spatial Processes, Institut national de recherche pour l’agriculture, l’alimentation et l’environnement, 84914 Avignon, France)

Abstract

We provide a framework to analyze control policies for the restless Markovian bandit model under both finite and infinite time horizons. We show that when the population of arms goes to infinity, the value of the optimal control policy converges to the solution of a linear program (LP). We provide necessary and sufficient conditions for a generic control policy to be (i) asymptotically optimal, (ii) asymptotically optimal with square root convergence rate, and (iii) asymptotically optimal with exponential rate. We then construct the LP-index policy that is asymptotically optimal with square root convergence rate on all models and with exponential rate if the model is nondegenerate in finite horizon and satisfies a uniform global attractor property in infinite horizon. We next define the LP-update policy, which is essentially a repeated LP-index policy that solves a new LP at each decision epoch. We conclude by providing numerical experiments to compare the efficiency of different LP-based policies.

Suggested Citation

  • Nicolas Gast & Bruno Gaujal & Chen Yan, 2024. "Linear Program-Based Policies for Restless Bandits: Necessary and Sufficient Conditions for (Exponentially Fast) Asymptotic Optimality," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2468-2491, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2468-2491
    DOI: 10.1287/moor.2022.0101
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2022.0101
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2022.0101?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
    ---><---

    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:ormoor:v:49:y:2024:i:4:p:2468-2491. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.