Off-policy evaluation often refers to two related tasks: estimating the expected return of a policy and estimating its value function (or other functions of interest, such as density ratios). While recent works on marginalized importance sampling (MIS) show that the former can enjoy provable guarantees under realizable function approximation, the latter is only known to be feasible under much stronger assumptions such as prohibitively expressive discriminators. In this work, we provide guarantees for off-policy function estimation under only realizability, by imposing proper regularization on the MIS objectives. Compared to commonly used regularization in MIS, our regularizer is much more flexible and can account for an arbitrary user-specified distribution, under which the learned function will be close to the groundtruth. We provide exact characterization of the optimal dual solution that needs to be realized by the discriminator class, which determines the data-coverage assumption in the case of value-function learning. As another surprising observation, the regularizer can be altered to relax the data-coverage requirement, and completely eliminate it in the ideal case with strong side information.

本文提供了在可行性前提下，通过在MIS目标上施加适当的规范化对离线策略函数估计提供保证，并提供了优化对偶解的确切特征化方法，该解决方案需要由鉴别器类实现，这决定了在值函数学习的情况下数据覆盖假设。

超越回报：基于用户指定的误差测量分布的离线策略评估