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Distributionally Robust Policy Learning with Wasserstein Distance

Author

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  • Daido Kido
Abstract
The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs assume that the available experimental or observational data are derived from the target population in which the estimated policy is implemented. However, this assumption often fails in practice because of limited useful data. In this case, policymakers must rely on the data generated in the source population, which differs from the target population. Unfortunately, existing estimation methods do not necessarily work as expected in the new setting, and strategies that can achieve a reasonable goal in such a situation are required. This study examines the application of distributionally robust optimization (DRO), which formalizes an ambiguity about the target population and adapts to the worst-case scenario in the set. It is shown that DRO with Wasserstein distance-based characterization of ambiguity provides simple intuitions and a simple estimation method. I then develop an estimator for the distributionally robust ITR and evaluate its theoretical performance. An empirical application shows that the proposed approach outperforms the naive approach in the target population.

Suggested Citation

  • Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2205.04637
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    References listed on IDEAS

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    1. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    2. Rajeev Dehejia & Cristian Pop-Eleches & Cyrus Samii, 2021. "From Local to Global: External Validity in a Fertility Natural Experiment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 217-243, January.
    3. Nathan Kallus, 2021. "More Efficient Policy Learning via Optimal Retargeting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 646-658, April.
    4. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    5. Toru Kitagawa & Aleksey Tetenov, 2021. "Equality-Minded Treatment Choice," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 561-574, March.
    6. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    7. Eva Vivalt, 2020. "How Much Can We Generalize From Impact Evaluations?," Journal of the European Economic Association, European Economic Association, vol. 18(6), pages 3045-3089.
    8. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    9. 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.
    10. 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.
    11. Friedlander, Daniel & Robins, Philip K, 1995. "Evaluating Program Evaluations: New Evidence on Commonly Used Nonexperimental Methods," American Economic Review, American Economic Association, vol. 85(4), pages 923-937, September.
    12. Hunt Allcott, 2015. "Site Selection Bias in Program Evaluation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(3), pages 1117-1165.
    13. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    14. Shapiro, Alexander, 2021. "Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 288(1), pages 1-13.
    15. Lant Pritchett, Justin Sandefur, 2013. "Context Matters for Size: Why External Validity Claims and Development Practice Don't Mix-Working Paper 336," Working Papers 336, Center for Global Development.
    16. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    17. Andrews, Isaiah & Oster, Emily, 2019. "A simple approximation for evaluating external validity bias," Economics Letters, Elsevier, vol. 178(C), pages 58-62.
    18. Weibin Mo & Zhengling Qi & Yufeng Liu, 2021. "Rejoinder: Learning Optimal Distributionally Robust Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 699-707, April.
    19. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    20. Elizabeth A. Stuart & Stephen R. Cole & Catherine P. Bradshaw & Philip J. Leaf, 2011. "The use of propensity scores to assess the generalizability of results from randomized trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(2), pages 369-386, April.
    21. Erin Hartman & Richard Grieve & Roland Ramsahai & Jasjeet S. Sekhon, 2015. "From sample average treatment effect to population average treatment effect on the treated: combining experimental with observational studies to estimate population treatment effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 757-778, June.
    22. Joseph Hotz, V. & Imbens, Guido W. & Mortimer, Julie H., 2005. "Predicting the efficacy of future training programs using past experiences at other locations," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 241-270.
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    Cited by:

    1. Toru Kitagawa & Hugo Lopez & Jeff Rowley, 2022. "Stochastic Treatment Choice with Empirical Welfare Updating," Papers 2211.01537, arXiv.org, revised Feb 2023.
    2. Yanqin Fan & Hyeonseok Park & Gaoqian Xu, 2023. "Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport," Papers 2307.00779, arXiv.org.

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