IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v334y2026i2p676-687.html

O(1/T) time-average convergence in a generalization of network zero-sum games via alternating gradient descent

Author

Listed:
  • Bailey, James P.

Abstract

Alternating methods have become more popular in online optimization due to theoretically obtained stability properties and empirical evidence of improved performance. We prove that alternating gradient descent (AGD) achieves O(1/T) time-average convergence to the set of Nash equilibria in unconstrained zero-sum games while using learning rates four times larger than those acceptable for optimistic gradient descent (OGD). We introduce a multiagent version of AGD and show that the optimization guarantees extend to this setting. Experimentally, we demonstrate that the time-averaged strategies are approximately 3.602 times closer to the set of Nash equilibria than OGD in the 2-agent setting and 1.901 times closer in the multiagent setting. Finally, we introduce a new generalization of network zero-sum games that is distinct from monotone games and includes games from every level of complexity of the rank-based hierarchy for bimatrix games. We show that our optimization guarantees extend to this generalization.

Suggested Citation

  • Bailey, James P., 2026. "O(1/T) time-average convergence in a generalization of network zero-sum games via alternating gradient descent," European Journal of Operational Research, Elsevier, vol. 334(2), pages 676-687.
    • Handle: RePEc:eee:ejores:v:334:y:2026:i:2:p:676-687
    DOI: 10.1016/j.ejor.2026.04.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221726003966
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2026.04.041?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:ejores:v:334:y:2026:i:2:p:676-687. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.