Model-based RL in Contextual Decision Processes: PAC bounds and Exponential Improvements over Model-free Approaches

We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample complexity governed by a new structural parameter called the witness rank, which we show to be small in several settings of interest, including factored MDPs and reactive POMDPs. We also show that the witness rank of a problem is never larger than the recently proposed Bellman rank parameter governing the sample complexity of the model-free algorithm OLIVE (Jiang et al., 2017), the only other provably sample efficient algorithm at this level of generality. Focusing on the special case of factored MDPs, we prove an exponential lower bound for a general class of model-free approaches, including OLIVE, which when combined with our algorithmic results demonstrates exponential separation between model-based and model-free RL in some rich-observation settings.