Understanding the Curse of Horizon in Off-Policy Evaluation via Conditional Importance Sampling

Yao Liu, Pierre-Luc Bacon, Emma Brunskill

Keywords: Reinforcement Learning - Theory

Abstract: Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of conditional Monte Carlo. Surprisingly, we find that in finite horizon MDPs there is no strict variance reduction of per-decision importance sampling or stationary importance sampling, comparing with vanilla importance sampling. We then provide sufficient conditions under which the per-decision or stationary estimators will provably reduce the variance over importance sampling with finite horizons. For the asymptotic (in terms of horizon $T$) case, we develop upper and lower bounds on the variance of those estimators which yields sufficient conditions under which there exists an exponential v.s. polynomial gap between the variance of importance sampling and that of the per-decision or stationary estimators. These results help advance our understanding of if and when new types of IS estimators will improve the accuracy of off-policy estimation.

This is an embedded video. Talk and the respective paper are published at ICML 2020 virtual conference. If you are one of the authors of the paper and want to manage your upload, see the question "My papertalk has been externally embedded..." in the FAQ section.


Post Comment
no comments yet
code of conduct: tbd

Similar Papers