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Several algorithms for learning near-optimal policies in Markov Decision Processes have been analyzed and proven efficient. Empirical results have suggested that Model-based Interval Estimation (MBIE) learns efficiently in practice, effectively balancing exploration and exploitation. This paper presents the first theoretical analysis of MBIE, proving its efficiency even under worst-case conditions. The paper also introduces a new performance metric, average loss, and relates it to its less "online" cousins from the literature.
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Strehl et al. (2005) studied this question.