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This paper proposes an incremental sparse Bayesian learning method to allow continuous dialog strategy learning from the interactions with real users. Since conventional reinforcement learning (RL) methods require a huge number of dialogs to reach convergence, it has been essential to use a simulated user in training dialog policies. The disadvantage of this approach is that the trained dialog policies always lag behind the optimal one for live users. In order to tackle this problem, a few studies applying online RL methods to dialog management have emerged and showed very promising results. However, these methods are limited to learning online the weight parameters of the basis functions in the model and so need batch learning on a fixed data set or some heuristics to find appropriate values for other meta parameters such as sparsity-controlling thresholds, basis function parameters, and noise parameters. The proposed method attempts to overcome this limitation to achieve fully incremental and fast dialog strategy learning by adopting a sparse Bayesian learning method for value function approximation. In order to verify the proposed method, three different experimental conditions have been used: artificial data, a simulated user, and real users. The experiment on the artificial data showed that the proposed method successfully learns all the parameters in an incremental manner. Also, the experiment on training and evaluating dialog policies with a simulated user clearly demonstrated that the proposed method is much faster than conventional RL methods. A live user study showed that the dialog strategy learned from real users performed as good as the best past systems, although it slightly underperformed the one trained on simulated dialogs due to the difficulty of user feedback elicitation.