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Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits

Author

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  • Keisuke Hirano
  • Jack R. Porter

Abstract

We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect the observation of variables in later stages, our asymptotic representation characterizes all limit distributions attainable through a joint choice of an adaptive design rule and statistics applied to the adaptively generated data. This facilitates local power analysis of tests, comparison of adaptive treatments rules, and other analyses of batchwise sequential statistical decision rules.

Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2302.03117
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    References listed on IDEAS

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    Cited by:

    1. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org, revised Apr 2025.
    2. Karun Adusumilli, 2023. "Optimal tests following sequential experiments," Papers 2305.00403, arXiv.org, revised Jun 2023.
    3. Masahiro Kato, 2023. "Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget," Papers 2310.19788, arXiv.org, revised Mar 2024.
    4. Karun Adusumilli & Abhi Vemulapati, 2026. "Designing Persuasive Experiments," Papers 2605.16703, arXiv.org, revised Jun 2026.

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