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

Karun Adusumilli

arXiv 28 Oct 2022 · Econometrics · publishedThe Review of Economic Studies (2025) · 1 citations (OpenAlex)

arXiv:2210.15841 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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 between 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 a continuous time limit, we characterize the optimal policies under the minimax regret criterion. We show that the same policies also remain optimal under both parametric and non-parametric outcome distributions in an asymptotic regime where sampling costs approach zero. The minimax optimal sampling rule is just the Neyman allocation: it is independent of sampling costs and does not adapt to observed outcomes. The decision-maker halts sampling when the product of the average treatment difference and the number of observations surpasses a specific threshold. The results derived also apply to the so-called best-arm identification problem, where the number of observations is exogenously specified.

Citation extraction

40
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Fudenberg, Strack and Strzalecki (2018) Speed, accuracy, and the optimal timing of choices1.00083100%
2Liang, Mu and Syrgkanis (2022) Dynamically aggregating diverse information1.00073100%
3Arrow, Blackwell and Girshick (1949) Bayes and minimax solutions of sequential decision problems0.9285480%
4Adusumilli (2021) Risk and optimal policies in bandit experiments self0.8229456%
5Wald (1947) Sequential analysis0.81142100%
6Morris and Strack (2019) The Wald problem and the relation of sequential sampling and ex-ante information costs0.7946450%
7Shiryaev (2007) Optimal stopping rules0.7639344%
8ksendal (2003) Stochastic differential equations0.7373367%
9Fan and Glynn (2021) Diffusion Approximations for Thompson Sampling0.73732100%
10Kuang and Wager (2024) Weak signal asymptotics for sequentially randomized experiments0.73732100%

Showing the top 10 of 40 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Optimizing Returns from Experimentation Programs0.40511
2On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models0.40511