Abstract

Off-policy estimation for long-horizon problems is important in many real-life applications such as healthcare and robotics, where high-fidelity simulators may not be available and on-policy evaluation is expensive or impossible. Recently, Liu et al. (2018) proposed an approach that avoids the curse of horizon suffered by typical importance-sampling-based methods. While showing promising results, this approach is limited in practice as it requires data be drawn from the stationary distribution of a known behavior policy. In this work, we propose a novel approach that eliminates such limitations. In particular, we formulate the problem as solving for the fixed point of a certain operator, and develop a new estimator that computes importance ratios of stationary distributions, without knowledge of how the off-policy data are collected. We analyze its asymptotic consistency and finite-sample generalization. Experiments on benchmarks verify the effectiveness of our approach.