We consider off-policy evaluation (OPE), which evaluates the performance of a new policy from observed data collected from previous experiments, without requiring the execution of the new policy. This finds important applications in areas with high execution cost or safety concerns, such as medical diagnosis, recommendation systems and robotics. In practice, due to the limited information from off-policy data, it is highly desirable to construct rigorous confidence intervals, not just point estimation, for the policy performance. In this work, we propose a new variational framework which reduces the problem of calculating tight confidence bounds in OPE into an optimization problem on a feasible set that catches the true state-action value function with high probability. The feasible set is constructed by leveraging statistical properties of a recently proposed kernel Bellman loss (Feng et al., 2019). We design an efficient computational approach for calculating our bounds, and extend it to perform post-hoc diagnosis and correction for existing estimators. Empirical results show that our method yields tight confidence intervals in different settings.
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