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

2020/10/08 by Masahiro Kato, Kato, Masahiro, Shota Yasui +3
Mathematics · Decision Sciences · #Statistical Methods and Inference #Advanced Statistical Process Monitoring #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2010.03792

Abstract

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

Citations

• Estimating causal effects of treatments in randomized and nonrandomized studies.
• Doubly Robust Estimation in Missing Data and Causal Inference Models
• Thompson Sampling for Contextual Bandits with Linear Payoffs
• Off-Policy Evaluation and Learning for External Validity under a\n Covariate Shift
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

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