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Understanding the Curse of Horizon in Off-Policy Evaluation via Conditional Importance Sampling
Yao Liu · Pierre-Luc Bacon · Emma Brunskill

Tue Jul 14 12:00 PM -- 12:45 PM & Tue Jul 14 11:00 PM -- 11:45 PM (PDT) @
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.

Author Information

Yao Liu (Stanford University)
Pierre-Luc Bacon (Stanford University)
Emma Brunskill (Stanford University)
Emma Brunskill

Emma Brunskill is an associate tenured professor in the Computer Science Department at Stanford University. Brunskill’s lab aims to create AI systems that learn from few samples to robustly make good decisions and is part of the Stanford AI Lab, the Stanford Statistical ML group, and AI Safety @Stanford. Brunskill has received a NSF CAREER award, Office of Naval Research Young Investigator Award, a Microsoft Faculty Fellow award and an alumni impact award from the computer science and engineering department at the University of Washington. Brunskill and her lab have received multiple best paper nominations and awards both for their AI and machine learning work (UAI best paper, Reinforcement Learning and Decision Making Symposium best paper twice) and for their work in Ai of education (Intelligent Tutoring Systems Conference, Educational Data Mining conference x3, CHI).

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