Anders Bredahl Kock, David Preinerstorfer, Bezirgen Veliyev
arXiv 19 May 2020 · Econometrics · publishedJournal of Econometrics (2022) · 3 citations (OpenAlex)
arXiv:2005.09717 · PDF · DOI · OpenAlex · Extracted main text
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 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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kock, A. B., D. Preinerstorfer, and B. Veliyev (2020) Functional sequential treatment allocation self | 1.000 | 7 | 3 | 100% |
| 2 | Bubeck, S., R. Munos, and G. Stoltz (2009) Pure exploration in multi-armed bandits problems | 1.000 | 5 | 3 | 100% |
| 3 | Kock, A. B., D. Preinerstorfer, and B. Veliyev (2020) Functional sequential treatment allocation with covariates self | 0.843 | 3 | 3 | 100% |
| 4 | Manski, C. F. and A. Tetenov (2016) Sufficient trial size to inform clinical practice | 0.737 | 3 | 2 | 100% |
| 5 | Audibert, J.-Y., S. Bubeck, and R. Munos (2010) Best arm identification in multi-armed bandits | 0.644 | 2 | 2 | 100% |
| 6 | Bélisle, C. and V. Melfi (2008) Independence after adaptive allocation | 0.644 | 2 | 2 | 100% |
| 7 | Karnin, Z., T. Koren, and O. Somekh (2013) Almost optimal exploration in multi-armed bandits | 0.644 | 2 | 2 | 100% |
| 8 | Manski, C. F (2004) Statistical treatment rules for heterogeneous populations | 0.644 | 2 | 2 | 100% |
| 9 | Tran-Thanh, L. and J. Y. Yu (2014) Functional bandits | 0.644 | 2 | 2 | 100% |
| 10 | Cassel, A., S. Mannor, and A. Zeevi (2018) A general approach to multi-armed bandits under risk criteria | 0.511 | 2 | 1 | 100% |
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