Doubly Robust Off-policy Evaluation for Reinforcement Learning

We study the problem of evaluating a policy that is different from the one that generates data. Such a problem, known as off-policy evaluation in reinforcement learning (RL), is encountered whenever one wants to estimate the value of a new solution, based on historical data, before actually deploying it in the real system, which is a critical step of applying RL in most real-world applications. Despite the fundamental importance of the problem, existing general methods either have uncontrolled bias or suffer high variance. In this work, we extend the so-called doubly robust estimator for bandits to sequential decision-making problems, which gets the best of both worlds: it is guaranteed to be unbiased and has low variance, and as a point estimator, it outperforms the most popular importance-sampling estimator and its variants in most occasions. We also provide theoretical results on the hardness of the problem, and show that our estimator can match the asymptotic lower bound in certain scenarios.