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Optimistic Posterior Sampling for Reinforcement Learning: Worst-Case Regret Bounds

Author

Listed:
  • Shipra Agrawal

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Randy Jia

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We present an algorithm based on posterior sampling (aka Thompson sampling) that achieves near-optimal worst-case regret bounds when the underlying Markov decision process (MDP) is communicating with a finite, although unknown, diameter. Our main result is a high probability regret upper bound of O ˜ ( D S A T ) for any communicating MDP with S states, A actions, and diameter D . Here, regret compares the total reward achieved by the algorithm to the total expected reward of an optimal infinite-horizon undiscounted average reward policy in time horizon T . This result closely matches the known lower bound of Ω ( DSAT ) . Our techniques involve proving some novel results about the anti-concentration of Dirichlet distribution, which may be of independent interest.

Suggested Citation

  • Shipra Agrawal & Randy Jia, 2023. "Optimistic Posterior Sampling for Reinforcement Learning: Worst-Case Regret Bounds," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 363-392, February.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:1:p:363-392
    DOI: 10.1287/moor.2022.1266
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