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Learning Optimal Distributionally Robust Individualized Treatment Rules

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  • Weibin Mo
  • Zhengling Qi
  • Yufeng Liu

Abstract

Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. Many existing methods assume that the training and testing distributions are the same. However, the estimated optimal ITR may have poor generalizability when the training and testing distributions are not identical. In this article, we consider the problem of finding an optimal ITR from a restricted ITR class where there are some unknown covariate changes between the training and testing distributions. We propose a novel distributionally robust ITR (DR-ITR) framework that maximizes the worst-case value function across the values under a set of underlying distributions that are “close” to the training distribution. The resulting DR-ITR can guarantee the performance among all such distributions reasonably well. We further propose a calibrating procedure that tunes the DR-ITR adaptively to a small amount of calibration data from a target population. In this way, the calibrated DR-ITR can be shown to enjoy better generalizability than the standard ITR based on our numerical studies. Supplementary materials for this article are available online.

Suggested Citation

  • Weibin Mo & Zhengling Qi & Yufeng Liu, 2021. "Learning Optimal Distributionally Robust Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 659-674, April.
  • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:534:p:659-674
    DOI: 10.1080/01621459.2020.1796359
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    Cited by:

    1. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    2. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org, revised Aug 2023.
    3. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    4. Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    5. Gao, Yuhe & Shi, Chengchun & Song, Rui, 2023. "Deep spectral Q-learning with application to mobile health," LSE Research Online Documents on Economics 119445, London School of Economics and Political Science, LSE Library.
    6. Christopher Adjaho & Timothy Christensen, 2022. "Externally Valid Policy Choice," Papers 2205.05561, arXiv.org, revised Jul 2023.

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