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There have been many recent advances on provably efficient ReinforcementLearning (RL) in problems with rich observation spaces. However, all theseworks share a strong realizability assumption about the optimal value functionof the true MDP. Such realizability assumptions are often too strong to hold inpractice. In this work, we consider the more realistic setting of agnostic RLwith rich observation spaces and a fixed class of policies $\Pi$ that may notcontain any near-optimal policy. We provide an algorithm for this setting whoseerror is bounded in terms of the rank $d$ of the underlying MDP. Specifically,our algorithm enjoys a sample complexity bound of $\widetilde{O}\left((H^{4d}K^{3d} \log |\Pi|)/\epsilon^2\right)$ where $H$ is the length of episodes, $K$is the number of actions and $\epsilon>0$ is the desired sub-optimality. Wealso provide a nearly matching lower bound for this agnostic setting that showsthat the exponential dependence on rank is unavoidable, without furtherassumptions.

Agnostic Reinforcement Learning with Low-Rank MDPs and Rich Observations