We study minimax methods for off-policy evaluation (OPE) using value-functions and marginalized importance weights. Despite that they hold promises of overcoming the exponential variance in traditional importance sampling, several key problems remain: (1) They require function approximation and are generally biased. For the sake of trustworthy OPE, is there anyway to quantify the biases? (2) They are split into two styles ("weight-learning" vs "value-learning"). Can we unify them? In this paper we answer both questions positively. By slightly altering the derivation of previous methods (one from each style; Uehara and Jiang, 2019), we unify them into a single confidence interval (CI) that automatically comes with a special type of double robustness: when either the value-function or importance weight class is well-specified, the CI is valid and its length quantifies the misspecification of the other class. We can also tell which class is misspecified, which provides useful diagnostic information for the design of function approximation. Our CI also provides a unified view of and new insights to some recent methods: for example, one side of the CI recovers a version of AlgaeDICE (Nachum et al., 2019b), and we show that the two sides need to be used together and either alone may incur doubled approximation error as a point estimate. We further examine the potential of applying these bounds to two long-standing problems: off-policy policy optimization with poor data coverage (i.e., exploitation), and efficient exploration. With a well-specified value-function class, we show that optimizing the lower and the upper bounds lead to good exploitation and exploration, respectively.

该研究使用价值函数和边际重要性权重研究了最小极小化方法在离线策略评估中的应用，结合两种不同风格的方法，提出了一个特殊类型的双重稳健方法，解决了偏见问题，同时还探索了其在数据覆盖不足的离线策略优化中对探索和开发的影响。

离线评估和策略优化的极小极大值区间