Doubly Robust Interval Estimation for Optimal Policy Evaluation in Online Learning
This work addresses policy evaluation for online learning in fields like medicine and economics, offering a method for real-time inference, but it is incremental as it builds on existing bandit algorithms and doubly robust techniques.
The paper tackles the challenge of evaluating the performance of an optimal policy in online learning with dependent data and unknown policies, by developing the DREAM method for doubly robust interval estimation, which provides asymptotically normal estimators and valid confidence intervals as demonstrated in simulations and real data.
Evaluating the performance of an ongoing policy plays a vital role in many areas such as medicine and economics, to provide crucial instructions on the early-stop of the online experiment and timely feedback from the environment. Policy evaluation in online learning thus attracts increasing attention by inferring the mean outcome of the optimal policy (i.e., the value) in real-time. Yet, such a problem is particularly challenging due to the dependent data generated in the online environment, the unknown optimal policy, and the complex exploration and exploitation trade-off in the adaptive experiment. In this paper, we aim to overcome these difficulties in policy evaluation for online learning. We explicitly derive the probability of exploration that quantifies the probability of exploring non-optimal actions under commonly used bandit algorithms. We use this probability to conduct valid inference on the online conditional mean estimator under each action and develop the doubly robust interval estimation (DREAM) method to infer the value under the estimated optimal policy in online learning. The proposed value estimator provides double protection for consistency and is asymptotically normal with a Wald-type confidence interval provided. Extensive simulation studies and real data applications are conducted to demonstrate the empirical validity of the proposed DREAM method.