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

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  • Keisuke Hirano
  • Jack R. Porter

Abstract

We develop asymptotic approximation results that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and other statistical decision problems that involve multiple decision nodes with structured and possibly endogenous information sets. Our results extend the classic asymptotic representation theorem used extensively in efficiency bound theory and local power analysis. In adaptive settings where the decision at one stage can affect the observation of variables in later stages, we show that a limiting data environment characterizes all limit distributions attainable through a joint choice of an adaptive design rule and statistics applied to the adaptively generated data, under local alternatives. We illustrate how the theory can be applied to study the choice of adaptive rules and end-of-sample statistical inference in batched (groupwise) sequential adaptive experiments.

Suggested Citation

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

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    Cited by:

    1. Karun Adusumilli, 2023. "Optimal tests following sequential experiments," Papers 2305.00403, arXiv.org, revised Jun 2023.
    2. Masahiro Kato, 2023. "Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget," Papers 2310.19788, arXiv.org, revised Mar 2024.

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