Off-policy evaluation provides an essential tool for evaluating the effects of different policies or treatments using only observed data. When applied to high-stakes scenarios such as medical diagnosis or financial decision-making, it is crucial to provide provably correct upper and lower bounds of the expected reward, not just a classical single point estimate, to the end-users, as executing a poor policy can be very costly. In this work, we propose a provably correct method for obtaining interval bounds for off-policy evaluation in a general continuous setting. The idea is to search for the maximum and minimum values of the expected reward among all the Lipschitz Q-functions that are consistent with the observations, which amounts to solving a constrained optimization problem on a Lipschitz function space. We go on to introduce a Lipschitz value iteration method to monotonically tighten the interval, which is simple yet efficient and provably convergent. We demonstrate the practical efficiency of our method on a range of benchmarks.

研究提出了用于获得一般连续情况下离线策略评估的区间界限的可证明正确的方法，该方法基于搜索与观察一致的所有Lipschitz Q函数中期望奖励的最大和最小值，进而引入了Lipschitz值迭代方法以加紧区间，可以在一定程度上提高部分高风险应用的效率。

利普希茨价值迭代的异策略区间估计