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How to sample and when to stop sampling: The generalized Wald problem and minimax policies

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  • Karun Adusumilli

Abstract

The aim of this paper is to develop techniques for incorporating the cost of information into experimental design. Specifically, we study sequential experiments where sampling is costly and a decision-maker aims to determine the best treatment for full scale implementation by (1) adaptively allocating units to two possible treatments, and (2) stopping the experiment when the expected welfare (inclusive of sampling costs) from implementing the chosen treatment is maximized. Working under the diffusion limit, we describe the optimal policies under the minimax regret criterion. Under small cost asymptotics, the same policies are also optimal under parametric and non-parametric distributions of outcomes. The minimax optimal sampling rule is just the Neyman allocation; it is independent of sampling costs and does not adapt to previous outcomes. The decision-maker stops sampling when the average difference between the treatment outcomes, multiplied by the number of observations collected until that point, exceeds a specific threshold. The results derived here also apply to best arm identification with two arms.

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  • Karun Adusumilli, 2022. "How to sample and when to stop sampling: The generalized Wald problem and minimax policies," Papers 2210.15841, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2210.15841
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    1. Drew Fudenberg & Philipp Strack & Tomasz Strzalecki, 2018. "Speed, Accuracy, and the Optimal Timing of Choices," American Economic Review, American Economic Association, vol. 108(12), pages 3651-3684, December.
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    Cited by:

    1. 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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