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Regret Analysis of a Markov Policy Gradient Algorithm for Multiarm Bandits

Author

Listed:
  • Neil Walton

    (Durham University Business School, Durham DH1 3LB, United Kingdom)

  • Denis Denisov

    (Durham University Business School, Durham DH1 3LB, United Kingdom)

Abstract

We consider a policy gradient algorithm applied to a finite-arm bandit problem with Bernoulli rewards. We allow learning rates to depend on the current state of the algorithm rather than using a deterministic time-decreasing learning rate. The state of the algorithm forms a Markov chain on the probability simplex. We apply Foster–Lyapunov techniques to analyze the stability of this Markov chain. We prove that, if learning rates are well-chosen, then the policy gradient algorithm is a transient Markov chain, and the state of the chain converges on the optimal arm with logarithmic or polylogarithmic regret.

Suggested Citation

  • Neil Walton & Denis Denisov, 2023. "Regret Analysis of a Markov Policy Gradient Algorithm for Multiarm Bandits," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1553-1588, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1553-1588
    DOI: 10.1287/moor.2022.1311
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