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Functional Sequential Treatment Allocation with Covariates

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  • Anders Bredahl Kock
  • David Preinerstorfer
  • Bezirgen Veliyev

Abstract

We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.

Suggested Citation

  • Anders Bredahl Kock & David Preinerstorfer & Bezirgen Veliyev, 2020. "Functional Sequential Treatment Allocation with Covariates," Papers 2001.10996, arXiv.org.
    • Handle: RePEc:arx:papers:2001.10996
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    References listed on IDEAS

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    1. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    2. Anders Bredahl Kock & David Preinerstorfer & Bezirgen Veliyev, 2022. "Functional Sequential Treatment Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1311-1323, September.
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    Cited by:

    1. Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org.
    2. Toru Kitagawa & Guanyi Wang, 2021. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," CeMMAP working papers CWP28/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Kitagawa, Toru & Wang, Guanyi, 2023. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," Journal of Econometrics, Elsevier, vol. 232(1), pages 109-131.
    4. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.

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