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Semi-Parametric Efficient Policy Learning with Continuous Actions

Author

Listed:
  • Mert Demirer
  • Vasilis Syrgkanis
  • Greg Lewis
  • Victor Chernozhukov
Abstract
We consider off-policy evaluation and optimization with continuous action spaces. We focus on observational data where the data collection policy is unknown and needs to be estimated. We take a semi-parametric approach where the value function takes a known parametric form in the treatment, but we are agnostic on how it depends on the observed contexts. We propose a doubly robust off-policy estimate for this setting and show that off-policy optimization based on this estimate is robust to estimation errors of the policy function or the regression model. Our results also apply if the model does not satisfy our semi-parametric form, but rather we measure regret in terms of the best projection of the true value function to this functional space. Our work extends prior approaches of policy optimization from observational data that only considered discrete actions. We provide an experimental evaluation of our method in a synthetic data example motivated by optimal personalized pricing and costly resource allocation.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1905.10116
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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. 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.
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    6. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    7. Graham, Bryan S. & Pinto, Cristine Campos de Xavier, 2022. "Semiparametrically efficient estimation of the average linear regression function," Journal of Econometrics, Elsevier, vol. 226(1), pages 115-138.
    8. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    9. 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.
    10. Athey, Susan & Wager, Stefan, 2017. "Efficient Policy Learning," Research Papers 3506, Stanford University, Graduate School of Business.
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    12. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
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    Citations

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    Cited by:

    1. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    3. 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.
    4. Yi Zhang & Kosuke Imai, 2023. "Individualized Policy Evaluation and Learning under Clustered Network Interference," Papers 2311.02467, arXiv.org, revised Feb 2024.
    5. Masahiro Kato & Masatoshi Uehara & Shota Yasui, 2020. "Off-Policy Evaluation and Learning for External Validity under a Covariate Shift," Papers 2002.11642, arXiv.org, revised Oct 2020.
    6. Masahiro Kato, 2020. "Confidence Interval for Off-Policy Evaluation from Dependent Samples via Bandit Algorithm: Approach from Standardized Martingales," Papers 2006.06982, arXiv.org.
    7. Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves," Papers 2010.04855, arXiv.org, revised Oct 2022.
    8. Ruohan Zhan & Shichao Han & Yuchen Hu & Zhenling Jiang, 2024. "Estimating Treatment Effects under Recommender Interference: A Structured Neural Networks Approach," Papers 2406.14380, arXiv.org, revised Jul 2024.
    9. Ruohan Zhan & Zhimei Ren & Susan Athey & Zhengyuan Zhou, 2024. "Policy Learning with Adaptively Collected Data," Management Science, INFORMS, vol. 70(8), pages 5270-5297, August.
    10. Ruohan Zhan & Zhimei Ren & Susan Athey & Zhengyuan Zhou, 2024. "Policy Learning with Adaptively Collected Data," Management Science, INFORMS, vol. 70(8), pages 5270-5297, August.
    11. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for Continuous Treatments," Papers 2402.02535, arXiv.org, revised Nov 2024.
    12. AmirEmad Ghassami & Andrew Ying & Ilya Shpitser & Eric Tchetgen Tchetgen, 2021. "Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference," Papers 2104.02929, arXiv.org, revised Mar 2022.
    13. 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.
    14. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2020. "Deep Learning for Individual Heterogeneity: An Automatic Inference Framework," Papers 2010.14694, arXiv.org, revised Jul 2021.
    15. Andrew Bennett & Nathan Kallus, 2020. "Efficient Policy Learning from Surrogate-Loss Classification Reductions," Papers 2002.05153, arXiv.org.

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