IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v49y2024i2p1241-1262.html
   My bibliography  Save this article

The Secretary Problem with Predictions

Author

Listed:
  • Kaito Fujii

    (National Institute of Informatics, Tokyo 101-8430, Japan)

  • Yuichi Yoshida

    (National Institute of Informatics, Tokyo 101-8430, Japan)

Abstract

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values are provided in advance. We propose an algorithm that achieves a nearly optimal value if the predictions are accurate and results in a constant-factor competitive ratio otherwise. We also show that the worst-case competitive ratio of an algorithm cannot be higher than some constant < 1 / e , which is the best possible competitive ratio when we ignore predictions, if the algorithm performs nearly optimally when the predictions are accurate. Additionally, for the multiple-choice secretary problem, we propose an algorithm with a similar theoretical guarantee. We empirically illustrate that if the predictions are accurate, the proposed algorithms perform well; meanwhile, if the predictions are inaccurate, performance is comparable to existing algorithms that do not use predictions.

Suggested Citation

  • Kaito Fujii & Yuichi Yoshida, 2024. "The Secretary Problem with Predictions," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 1241-1262, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:1241-1262
    DOI: 10.1287/moor.2022.0031
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2022.0031
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2022.0031?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:2:p:1241-1262. 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.