Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation
This addresses a critical bottleneck in reinforcement learning for long-term decision-making, offering a solution to a well-known issue with incremental methodological innovation.
The paper tackles the high variance problem in off-policy estimation for infinite-horizon tasks by proposing a method that applies importance sampling on stationary state-visitation distributions, avoiding unbounded variance and showing empirical improvements.
We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased estimators, but is known to suffer from an excessively high variance in long-horizon problems. In the extreme case of in infinite-horizon problems, the variance of an IS-based estimator may even be unbounded. In this paper, we propose a new off-policy estimation method that applies IS directly on the stationary state-visitation distributions to avoid the exploding variance issue faced by existing estimators.Our key contribution is a novel approach to estimating the density ratio of two stationary distributions, with trajectories sampled from only the behavior distribution. We develop a mini-max loss function for the estimation problem, and derive a closed-form solution for the case of RKHS. We support our method with both theoretical and empirical analyses.