IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.02535.html
   My bibliography  Save this paper

Data-driven Policy Learning for Continuous Treatments

Author

Listed:
  • Chunrong Ai
  • Yue Fang
  • Haitian Xie

Abstract

This paper studies policy learning for continuous treatments from observational data. Continuous treatments present more significant challenges than discrete ones because population welfare may need nonparametric estimation, and policy space may be infinite-dimensional and may satisfy shape restrictions. We propose to approximate the policy space with a sequence of finite-dimensional spaces and, for any given policy, obtain the empirical welfare by applying the kernel method. We consider two cases: known and unknown propensity scores. In the latter case, we allow for machine learning of the propensity score and modify the empirical welfare to account for the effect of machine learning. The learned policy maximizes the empirical welfare or the modified empirical welfare over the approximating space. In both cases, we modify the penalty algorithm proposed in \cite{mbakop2021model} to data-automate the tuning parameters (i.e., bandwidth and dimension of the approximating space) and establish an oracle inequality for the welfare regret.

Suggested Citation

  • Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for Continuous Treatments," Papers 2402.02535, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2402.02535
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2402.02535
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guanhua Chen & Donglin Zeng & Michael R. Kosorok, 2016. "Personalized Dose Finding Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1509-1521, October.
    2. 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.
    3. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    4. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
    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. Cai, Hengrui & Shi, Chengchun & Song, Rui & Lu, Wenbin, 2023. "Jump interval-learning for individualized decision making with continuous treatments," LSE Research Online Documents on Economics 118231, London School of Economics and Political Science, LSE Library.
    7. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    8. Jinzhi Bu & David Simchi-Levi & Li Wang, 2023. "Offline Pricing and Demand Learning with Censored Data," Management Science, INFORMS, vol. 69(2), pages 885-903, February.
    9. Juliana Schulz & Erica E. M. Moodie, 2021. "Doubly Robust Estimation of Optimal Dosing Strategies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 256-268, March.
    10. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    11. E. B. Laber & Y. Q. Zhao, 2015. "Tree-based methods for individualized treatment regimes," Biometrika, Biometrika Trust, vol. 102(3), pages 501-514.
    12. 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.
    13. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    14. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    15. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
    16. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    17. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    18. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    19. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    20. Carlos A. Flores & Alfonso Flores-Lagunes & Arturo Gonzalez & Todd C. Neumann, 2012. "Estimating the Effects of Length of Exposure to Instruction in a Training Program: The Case of Job Corps," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 153-171, February.
    21. Brantly Callaway & Weige Huang, 2020. "Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(4), pages 808-842, August.
    22. Xin Zhou & Nicole Mayer-Hamblett & Umer Khan & Michael R. Kosorok, 2017. "Residual Weighted Learning for Estimating Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 169-187, January.
    23. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    24. Bartlett, Peter L., 2008. "Fast Rates For Estimation Error And Oracle Inequalities For Model Selection," Econometric Theory, Cambridge University Press, vol. 24(2), pages 545-552, April.
    25. Mert Demirer & Vasilis Syrgkanis & Greg Lewis & Victor Chernozhukov, 2019. "Semi-Parametric Efficient Policy Learning with Continuous Actions," Papers 1905.10116, arXiv.org, revised Jul 2019.
    26. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    2. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    3. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    4. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    5. Toru Kitagawa & Weining Wang & Mengshan Xu, 2022. "Policy Choice in Time Series by Empirical Welfare Maximization," Papers 2205.03970, arXiv.org, revised Jun 2023.
    6. Davide Viviano & Jess Rudder, 2020. "Policy design in experiments with unknown interference," Papers 2011.08174, arXiv.org, revised May 2024.
    7. 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.
    8. Manski, Charles F., 2023. "Probabilistic prediction for binary treatment choice: With focus on personalized medicine," Journal of Econometrics, Elsevier, vol. 234(2), pages 647-663.
    9. Anders Bredahl Kock & David Preinerstorfer, 2024. "Regularizing Discrimination in Optimal Policy Learning with Distributional Targets," Papers 2401.17909, arXiv.org.
    10. 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.
    11. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    13. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    14. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Aug 2024.
    15. Charles F. Manski, 2021. "Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald," Econometrica, Econometric Society, vol. 89(6), pages 2827-2853, November.
    16. Augustine Denteh & Helge Liebert, 2022. "Who Increases Emergency Department Use? New Insights from the Oregon Health Insurance Experiment," Papers 2201.07072, arXiv.org, revised Apr 2023.
    17. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    18. Yuya Sasaki & Takuya Ura, 2020. "Welfare Analysis via Marginal Treatment Effects," Papers 2012.07624, arXiv.org.
    19. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    20. Davide Viviano & Jelena Bradic, 2020. "Fair Policy Targeting," Papers 2005.12395, arXiv.org, revised Jun 2022.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2402.02535. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.