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Neyman allocation is minimax optimal for best arm identification with two arms

Karun Adusumilli

arXiv 12 Apr 2022 · Econometrics

arXiv:2204.05527 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This note describes the optimal policy rule, according to the local asymptotic minimax regret criterion, for best arm identification when there are only two treatments. It is shown that the optimal sampling rule is the Neyman allocation, which allocates a constant fraction of units to each treatment in a manner that is proportional to the standard deviation of the treatment outcomes. When the variances are equal, the optimal ratio is one-half. This policy is independent of the data, so there is no adaptation to previous outcomes. At the end of the experiment, the policy maker adopts the treatment with higher average outcomes.

Citation extraction

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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
1K. Adusumilli, “Risk and optimal policies in bandit experiments,” ar… (2021) Risk and optimal policies in bandit experiments1.00073100%
2K. Hirano and J. R. Porter, “Asymptotics for statistical treatment r… (2009) Asymptotics for statistical treatment rules0.81142100%
3A. W. Van der Vaart, Asymptotic statistics. 1em plus 0.5em minus 0.4… (2000)0.58531100%
4A. Carpentier and A. Locatelli, “Tight (lower) bounds for the fixed… (2016) Tight (lower) bounds for the fixed budget best arm identification bandit problem0.51121100%
5D. Russo, “Simple bayesian algorithms for best arm identification,”… (2016) Simple bayesian algorithms for best arm identification0.51121100%
6A. N. Shiryaev, Optimal stopping rules. 1em plus 0.5em minus 0.4em S… (2007) vol. 80.51121100%
7J. Stoye, “New perspectives on statistical decisions under ambiguity… (2012) New perspectives on statistical decisions under ambiguity0.51121100%
8C.-H. Chen, J. Lin, E. Yücesan, and S. E. Chick, “Simulation budget… (2000) Simulation budget allocation for further enhancing the efficiency of ordinal optimization0.40511100%
chick2012sequentialunmatched citation key chick2012sequential0.40511100%
10A. Garivier and E. Kaufmann, “Optimal best arm identification with f… (2016) Optimal best arm identification with fixed confidence0.40511100%

Showing the top 10 of 17 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.

Cited by, within the corpus

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

Citing paperIntensityMentionsSections
1Best Arm Identification with Contextual Information under a Small Gap0.64422
2Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification0.40511
3Optimizing Returns from Experimentation Programs0.40511