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.
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