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Finding the Best Dueler

Author

Listed:
  • Zhengu Zhang

    (Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA
    These authors contributed equally to this work.)

  • Sheldon M. Ross

    (Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA
    These authors contributed equally to this work.)

Abstract

Consider a set of n players. We suppose that each game involves two players, that there is some unknown player who wins each game it plays with a probability greater than 1 / 2 , and that our objective is to determine this best player. Under the requirement that the policy employed guarantees a correct choice with a probability of at least some specified value, we look for a policy that has a relatively small expected number of games played before decision. We consider this problem both under the assumption that the best player wins each game with a probability of at least some specified value p 0 > 1 / 2 , and under a Bayesian assumption that the probability that player i wins a game against player j is v i v i + v j , where v 1 , … , v n are the unknown values of n independent and identically distributed exponential random variables. In the former case, we propose a policy where chosen pairs play a match that ends when one of them has had a specified number of wins more than the other; in the latter case, we propose a Thompson sampling type rule.

Suggested Citation

  • Zhengu Zhang & Sheldon M. Ross, 2023. "Finding the Best Dueler," Mathematics, MDPI, vol. 11(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1568-:d:1105376
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    Keywords

    best arm identification; dueling bandit;

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