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Designing the dialogue policy of a spoken dialogue system involves many nontrivial choices. This paper presents a reinforcement learning approach for automatically optimizing a dialogue policy, which addresses the technical challenges in applying reinforcement learning to a working dialogue system with human users. We report on the design, construction and empirical evaluation of NJFun, an experimental spoken dialogue system that provides users with access to information about fun things to do in New Jersey. Our results show that by optimizing its performance via reinforcement learning, NJFun measurably improves system performance.