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Multiplayer Bandits Without Observing Collision Information

Author

Listed:
  • Gábor Lugosi

    (Department of Economics and Business, Pompeu Fabra University, Barcelona 08010, Spain; Barcelona Graduate School of Economics, Barcelona 08005, Spain; ICREA, Pg. Lluís Companys 23, Barcelona 08010, Spain)

  • Abbas Mehrabian

    (School of Computer Science, McGill University, Montréal, Quebec H3A 0E9, Canada)

Abstract

We study multiplayer stochastic multiarmed bandit problems in which the players cannot communicate, and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider two feedback models: a model in which the players can observe whether a collision has occurred and a more difficult setup in which no collision information is available. We give the first theoretical guarantees for the second model: an algorithm with a logarithmic regret and an algorithm with a square-root regret that does not depend on the gaps between the means. For the first model, we give the first square-root regret bounds that do not depend on the gaps. Building on these ideas, we also give an algorithm for reaching approximate Nash equilibria quickly in stochastic anticoordination games.

Suggested Citation

  • Gábor Lugosi & Abbas Mehrabian, 2022. "Multiplayer Bandits Without Observing Collision Information," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1247-1265, May.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:2:p:1247-1265
    DOI: 10.1287/moor.2021.1168
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