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The goal of off-policy evaluation (OPE) is to evaluate a new policy usinghistorical data obtained via a behavior policy. However, because the contextualbandit algorithm updates the policy based on past observations, the samples arenot independent and identically distributed (i.i.d.). This paper tackles thisproblem by constructing an estimator from a martingale difference sequence(MDS) for the dependent samples. In the data-generating process, we do notassume the convergence of the policy, but the policy uses the same conditionalprobability of choosing an action during a certain period. Then, we derive anasymptotically normal estimator of the value of an evaluation policy. Asanother advantage of our method, the batch-based approach simultaneously solvesthe deficient support problem. Using benchmark and real-world datasets, weexperimentally confirm the effectiveness of the proposed method.

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