To evaluate prospective contextual bandit policies when experimentation is not possible, practitioners often rely on off-policy evaluation, using data collected under a behavioral policy. While off-policy evaluation studies typically focus on the expected return, practitioners often care about other functionals of the reward distribution (e.g., to express aversion to risk). In this paper, we first introduce the class of Lipschitz risk functionals, which subsumes many common functionals, including variance, mean-variance, and conditional value-at-risk (CVaR). For Lipschitz risk functionals, the error in off-policy risk estimation is bounded by the error in off-policy estimation of the cumulative distribution function (CDF) of rewards. Second, we propose Off-Policy Risk Assessment (OPRA), an algorithm that (i) estimates the target policy's CDF of rewards; and (ii) generates a plug-in estimate of the risk. Given a collection of Lipschitz risk functionals, OPRA provides estimates for each with corresponding error bounds that hold simultaneously. We analyze both importance sampling and variance-reduced doubly robust estimators of the CDF. Our primary theoretical contributions are (i) the first concentration inequalities for both types of CDF estimators and (ii) guarantees on our Lipschitz risk functional estimates, which converge at a rate of O(1/\sqrt{n}). For practitioners, OPRA offers a practical solution for providing high-confidence assessments of policies using a collection of relevant metrics.

该论文提出了一种基于Lipschitz风险函数的离线策略评估框架，使用OPRA估算目标策略的CDF，提供了对任何Lipschitz风险集合的插值估计，具有同时保证整个类的有限样本保证，并使用重要性采样和双重稳健估计实例化OPRA。

上下文臂带中的离线风险评估