  Off-Policy evaluation (OPE) is concerned with evaluating a new target policy
using offline data generated by a potentially different behavior policy. It is
critical in a number of sequential decision making problems ranging from
healthcare to technology industries. Most of the work in existing literature is
focused on evaluating the mean outcome of a given policy, and ignores the
variability of the outcome. However, in a variety of applications, criteria
other than the mean may be more sensible. For example, when the reward
distribution is skewed and asymmetric, quantile-based metrics are often
preferred for their robustness. In this paper, we propose a doubly-robust
inference procedure for quantile OPE in sequential decision making and study
its asymptotic properties. In particular, we propose utilizing state-of-the-art
deep conditional generative learning methods to handle parameter-dependent
nuisance function estimation. We demonstrate the advantages of this proposed
estimator through both simulations and a real-world dataset from a short-video
platform. In particular, we find that our proposed estimator outperforms
classical OPE estimators for the mean in settings with heavy-tailed reward
distributions.
