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The Adaptive Doubly Robust Estimator for Policy Evaluation in Adaptive Experiments and a Paradox Concerning Logging Policy

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  • Masahiro Kato
  • Shota Yasui
  • Kenichiro McAlinn

Abstract

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.

Suggested Citation

  • Masahiro Kato & Shota Yasui & Kenichiro McAlinn, 2020. "The Adaptive Doubly Robust Estimator for Policy Evaluation in Adaptive Experiments and a Paradox Concerning Logging Policy," Papers 2010.03792, arXiv.org, revised Jun 2021.
    • Handle: RePEc:arx:papers:2010.03792
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    References listed on IDEAS

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    1. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    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.
    3. 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.
    4. Masahiro Kato, 2020. "Confidence Interval for Off-Policy Evaluation from Dependent Samples via Bandit Algorithm: Approach from Standardized Martingales," Papers 2006.06982, arXiv.org.
    5. Yusuke Narita & Shota Yasui & Kohei Yata, 2018. "Efficient Counterfactual Learning from Bandit Feedback," Cowles Foundation Discussion Papers 2155, Cowles Foundation for Research in Economics, Yale University.
    6. Athey, Susan & Wager, Stefan, 2017. "Efficient Policy Learning," Research Papers 3506, Stanford University, Graduate School of Business.
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    Cited by:

    1. Masahiro Kato, 2021. "Adaptive Doubly Robust Estimator from Non-stationary Logging Policy under a Convergence of Average Probability," Papers 2102.08975, arXiv.org, revised Mar 2021.
    2. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2022. "Best Arm Identification with Contextual Information under a Small Gap," Papers 2209.07330, arXiv.org, revised Jan 2023.
    3. Masahiro Kato & Masaaki Imaizumi & Takuya Ishihara & Toru Kitagawa, 2023. "Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds," Papers 2302.02988, arXiv.org, revised Jul 2023.

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