Treatment recommendation with distributional targets

Anders Kock, David Preinerstorfer and Bezirgen Veliyev

Journal of Econometrics, 2023, vol. 234, issue 2, 624-646

Abstract: We study the problem of a decision maker who must provide the best possible treatment recommendation based on an experiment. The desirability of the outcome distribution resulting from the policy recommendation is measured through a functional capturing the distributional characteristic that the decision maker is interested in optimizing. This could be, e.g., its inherent inequality, welfare, level of poverty or its distance to a desired outcome distribution. If the functional of interest is not quasi-convex or if there are constraints, the optimal recommendation may be a mixture of treatments. This vastly expands the set of recommendations that must be considered. We characterize the difficulty of the problem by obtaining maximal expected regret lower bounds. Furthermore, we propose two (near) regret-optimal policies. The first policy is static and thus applicable irrespectively of the subjects arriving sequentially or not in the course of the experimentation phase. The second policy can utilize that subjects arrive sequentially by successively eliminating inferior treatments and thus spends the sampling effort where it is most needed.

Keywords: Treatment allocation; Pure exploration; Best treatment identification; Statistical decision theory; Nonparametric multi-armed bandit (search for similar items in EconPapers)
JEL-codes: C18 C21 C44 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:234:y:2023:i:2:p:624-646

DOI: 10.1016/j.jeconom.2022.08.003

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