Hierarchical decomposition promises to help scale reinforcement learning algorithms naturally to real-world problems by exploiting their underlying structure. Model-based algorithms, which provided the first finite-time convergence guarantees for reinforcement learning, may also play an important role in coping with the relative scarcity of data in large environments. In this paper, we introduce an algorithm that fully integrates modern hierarchical and model-learning methods in the standard

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... nforcement learning setting. Our algorithm, R-MAXQ, inherits the efficient modelbased exploration of the R-MAX algorithm and the opportunities for abstraction provided by the MAXQ framework. We analyze the sample complexity of our algorithm, and our experiments in a standard simulation environment illustrate the advantages of combining hierarchies and models.