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Off-Policy Evaluation of Bandit Algorithm from Dependent Samples under Batch Update Policy

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  • Masahiro Kato
  • Yusuke Kaneko

Abstract

The goal of off-policy evaluation (OPE) is to evaluate a new policy using historical data obtained via a behavior policy. However, because the contextual bandit algorithm updates the policy based on past observations, the samples are not independent and identically distributed (i.i.d.). This paper tackles this problem by constructing an estimator from a martingale difference sequence (MDS) for the dependent samples. In the data-generating process, we do not assume the convergence of the policy, but the policy uses the same conditional probability of choosing an action during a certain period. Then, we derive an asymptotically normal estimator of the value of an evaluation policy. As another advantage of our method, the batch-based approach simultaneously solves the deficient support problem. Using benchmark and real-world datasets, we experimentally confirm the effectiveness of the proposed method.

Suggested Citation

  • Masahiro Kato & Yusuke Kaneko, 2020. "Off-Policy Evaluation of Bandit Algorithm from Dependent Samples under Batch Update Policy," Papers 2010.13554, arXiv.org.
    • Handle: RePEc:arx:papers:2010.13554
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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. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    4. 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.
    5. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
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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. Davide Viviano & Jess Rudder, 2020. "Policy design in experiments with unknown interference," Papers 2011.08174, arXiv.org, revised May 2024.

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