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Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling

Author

Listed:
  • Kaito Ariu
  • Masahiro Kato
  • Junpei Komiyama
  • Kenichiro McAlinn
  • Chao Qin

Abstract

We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design. Theorem 1 of Kasy and Sautmann (2021) provides three asymptotic results that give theoretical guarantees for exploration sampling developed for this setting. We first show that the proof of Theorem 1 (1) has technical issues, and the proof and statement of Theorem 1 (2) are incorrect. We then show, through a counterexample, that Theorem 1 (3) is false. For the former two, we correct the statements and provide rigorous proofs. For Theorem 1 (3), we propose an alternative objective function, which we call posterior weighted policy regret, and derive the asymptotic optimality of exploration sampling.

Suggested Citation

  • Kaito Ariu & Masahiro Kato & Junpei Komiyama & Kenichiro McAlinn & Chao Qin, 2021. "Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling," Papers 2109.08229, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2109.08229
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    Cited by:

    1. Masahiro Kato, 2024. "Adaptive Generalized Neyman Allocation: Local Asymptotic Minimax Optimal Best Arm Identification," Papers 2405.19317, arXiv.org.
    2. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2022. "Best Arm Identification with Contextual Information under a Small Gap," Papers 2209.07330, arXiv.org, revised Jan 2023.
    3. Chao Qin & Daniel Russo, 2024. "Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification," Papers 2402.10592, arXiv.org, revised Jul 2024.
    4. Masahiro Kato, 2023. "Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget," Papers 2310.19788, arXiv.org, revised Mar 2024.
    5. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2023. "Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds," Papers 2302.02988, arXiv.org, revised Jul 2023.
    6. Toru Kitagawa & Jeff Rowley, 2024. "Bandit algorithms for policy learning: methods, implementation, and welfare-performance," The Japanese Economic Review, Springer, vol. 75(3), pages 407-447, July.
    7. Masahiro Kato & Kyohei Okumura & Takuya Ishihara & Toru Kitagawa, 2024. "Adaptive Experimental Design for Policy Learning," Papers 2401.03756, arXiv.org, revised Feb 2024.
    8. Masahiro Kato, 2023. "Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances," Papers 2312.12741, arXiv.org, revised Mar 2024.

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