IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v70y2022i3p1428-1447.html
   My bibliography  Save this article

Quantile Markov Decision Processes

Author

Listed:
  • Xiaocheng Li

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Huaiyang Zhong

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Margaret L. Brandeau

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific quantile of the cumulative reward instead of its expectation. In this paper, we consider the problem of optimizing the quantiles of the cumulative rewards of an MDP, which we refer to as a quantile Markov decision process (QMDP). We provide analytical results characterizing the optimal QMDP value function and present a dynamic programming-based algorithm to solve for the optimal policy. The algorithm also extends to the MDP problem with a conditional value-at-risk objective. We illustrate the practical relevance of our model by evaluating it on an HIV treatment initiation problem, in which patients aim to balance the potential benefits and risks of the treatment.

Suggested Citation

  • Xiaocheng Li & Huaiyang Zhong & Margaret L. Brandeau, 2022. "Quantile Markov Decision Processes," Operations Research, INFORMS, vol. 70(3), pages 1428-1447, May.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:3:p:1428-1447
    DOI: 10.1287/opre.2021.2123
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2021.2123
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2021.2123?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:oropre:v:70:y:2022:i:3:p:1428-1447. 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.