ReVar: Strengthening policy evaluation via reduced variance sampling.

This paper studies the problem of data collection for policy evaluation in Markov decision processes (MDPs). In policy evaluation, we are given a \textit{target} policy and asked to estimate the expected cumulative reward it will obtain in an environment formalized as an MDP. We develop theory for optimal data collection within the class of tree-structured MDPs by first deriving an oracle exploration strategy that uses knowledge of the variance of the reward distributions. We then introduce the \textbf{Re}duced \textbf{Var}iance Sampling (\rev\!) algorithm that approximates the oracle strategy when the reward variances are unknown a priori and bound its sub-optimality compared to the oracle strategy. Finally, we empirically validate that \rev leads to policy evaluation with mean squared error comparable to the oracle strategy and significantly lower than simply running the target policy.