arXiv 28 Oct 2022 · Econometrics · publishedThe Review of Economic Studies (2025) · 1 citations (OpenAlex)
arXiv:2210.15841 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fudenberg, Strack and Strzalecki (2018) Speed, accuracy, and the optimal timing of choices | 1.000 | 8 | 3 | 100% |
| 2 | Liang, Mu and Syrgkanis (2022) Dynamically aggregating diverse information | 1.000 | 7 | 3 | 100% |
| 3 | Arrow, Blackwell and Girshick (1949) Bayes and minimax solutions of sequential decision problems | 0.928 | 5 | 4 | 80% |
| 4 | Adusumilli (2021) Risk and optimal policies in bandit experiments self | 0.822 | 9 | 4 | 56% |
| 5 | Wald (1947) Sequential analysis | 0.811 | 4 | 2 | 100% |
| 6 | Morris and Strack (2019) The Wald problem and the relation of sequential sampling and ex-ante information costs | 0.794 | 6 | 4 | 50% |
| 7 | Shiryaev (2007) Optimal stopping rules | 0.763 | 9 | 3 | 44% |
| 8 | ksendal (2003) Stochastic differential equations | 0.737 | 3 | 3 | 67% |
| 9 | Fan and Glynn (2021) Diffusion Approximations for Thompson Sampling | 0.737 | 3 | 2 | 100% |
| 10 | Kuang and Wager (2024) Weak signal asymptotics for sequentially randomized experiments | 0.737 | 3 | 2 | 100% |
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Optimizing Returns from Experimentation Programs | 0.405 | 1 | 1 |
| 2 | On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models | 0.405 | 1 | 1 |