We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and value function classes exclusively through standard optimization primitives -- and therefore represent computationally efficient alternatives to prior algorithms that require enumeration. With stochastic hidden state dynamics, we prove that the only known sample-efficient algorithm, OLIVE, cannot be implemented in the oracle model. We also present several examples that illustrate fundamental challenges of tractable PAC reinforcement learning in such general settings.
State abstraction (or state aggregation) has been extensively studied in the fields of artificial intelligence and operations research. Instead of working in the ground state space, the decision maker usually finds solutions in the abstract state space much faster by treating groups of states as a unit by ignoring irrelevant state information. A number of abstractions have been proposed and studied in the reinforcement-learning and planning literatures, and positive and negative results are known. We provide a unified treatment of state abstraction for Markov decision processes. We study five particular abstraction schemes, some of which have been proposed in the past in different forms, and analyze their usability for planning and learning.