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Admissibility of Completely Randomized Trials: A Large-Deviation Approach

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  • Guido Imbens
  • Chao Qin
  • Stefan Wager

Abstract

When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the experimenter aims to allocate measurement efforts judiciously to confidently deploy the most effective treatment arm. We find that, whenever there are at least three treatment arms, there exist simple adaptive designs that universally and strictly dominate non-adaptive completely randomized trials. This dominance is characterized by a notion called efficiency exponent, which quantifies a design's statistical efficiency when the experimental sample is large. Our analysis focuses on the class of batched arm elimination designs, which progressively eliminate underperforming arms at pre-specified batch intervals. We characterize simple sufficient conditions under which these designs universally and strictly dominate completely randomized trials. These results resolve the second open problem posed in Qin [2022].

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  • Guido Imbens & Chao Qin & Stefan Wager, 2025. "Admissibility of Completely Randomized Trials: A Large-Deviation Approach," Papers 2506.05329, arXiv.org.
    • Handle: RePEc:arx:papers:2506.05329
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    File URL: http://arxiv.org/pdf/2506.05329
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    References listed on IDEAS

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    1. A Stefano Caria & Grant Gordon & Maximilian Kasy & Simon Quinn & Soha Osman Shami & Alexander Teytelboym, 2024. "An Adaptive Targeted Field Experiment: Job Search Assistance for Refugees in Jordan," Journal of the European Economic Association, European Economic Association, vol. 22(2), pages 781-836.
    2. Dean Karlan & John A. List, 2007. "Does Price Matter in Charitable Giving? Evidence from a Large-Scale Natural Field Experiment," American Economic Review, American Economic Association, vol. 97(5), pages 1774-1793, December.
    3. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    4. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, Enero-Abr.
    5. 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.
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