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Functional Sequential Treatment Allocation

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  • Anders Bredahl Kock
  • David Preinerstorfer
  • Bezirgen Veliyev

Abstract

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present article, we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1311-1323
    DOI: 10.1080/01621459.2020.1851236
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    Cited by:

    1. 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.
    2. Maximilian Kasy & Anja Sautmann, 2021. "Adaptive Treatment Assignment in Experiments for Policy Choice," Econometrica, Econometric Society, vol. 89(1), pages 113-132, January.
    3. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    4. Anders Bredahl Kock & David Preinerstorfer, 2024. "Regularizing Discrimination in Optimal Policy Learning with Distributional Targets," Papers 2401.17909, arXiv.org.
    5. Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org.
    6. Toru Kitagawa & Guanyi Wang, 2020. "Who Should Get Vaccinated? Individualized Allocation of Vaccines Over SIR Network," Papers 2012.04055, arXiv.org, revised Jul 2021.
    7. Michael Lechner, 2023. "Causal Machine Learning and its use for public policy," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 159(1), pages 1-15, December.
    8. 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.
    9. Toru Kitagawa & Guanyi Wang, 2020. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," CeMMAP working papers CWP59/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Anders Bredahl Kock & David Preinerstorfer & Bezirgen Veliyev, 2020. "Functional Sequential Treatment Allocation with Covariates," Papers 2001.10996, arXiv.org.
    11. Toru Kitagawa & Jeff Rowley, 2024. "Bandit algorithms for policy learning: methods, implementation, and welfare-performance," The Japanese Economic Review, Springer, vol. 75(3), pages 407-447, July.
    12. Claudio Cardoso Flores & Marcelo Cunha Medeiros, 2020. "Online Action Learning in High Dimensions: A Conservative Perspective," Papers 2009.13961, arXiv.org, revised Mar 2024.

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