Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process
本文研究如何利用观测数据为无限时域下的目标策略价值构建置信区间，通过引入辅助变量解决未观测混杂问题，并开发了鲁棒的离策略价值估计器。
This article is concerned with constructing a confidence interval for a target policy’s value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this article, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy’s value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies. A Python implementation of the proposed procedure is available at https://github.com/Mamba413/cope.