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Accurately evaluating new policies (e.g. ad-placement models, rankingfunctions, recommendation functions) is one of the key prerequisites forimproving interactive systems. While the conventional approach to evaluationrelies on online A/B tests, recent work has shown that counterfactualestimators can provide an inexpensive and fast alternative, since they can beapplied offline using log data that was collected from a different policyfielded in the past. In this paper, we address the question of how to estimatethe performance of a new target policy when we have log data from multiplehistoric policies. This question is of great relevance in practice, sincepolicies get updated frequently in most online systems. We show that naivelycombining data from multiple logging policies can be highly suboptimal. Inparticular, we find that the standard Inverse Propensity Score (IPS) estimatorsuffers especially when logging and target policies diverge -- to a point wherethrowing away data improves the variance of the estimator. We therefore proposetwo alternative estimators which we characterize theoretically and compareexperimentally. We find that the new estimators can provide substantiallyimproved estimation accuracy.

Effective Evaluation using Logged Bandit Feedback from Multiple Loggers