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

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