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This paper addresses the problem of feature selection in the reinforcement learning (RL) of the dialog policies of spoken dialog systems. A statistical dialog manager selects the system actions the system should take based on the features derived from the current dialog state and/or the system's belief state. When defining the features used by the system for training the dialog policy, however, finding a set of actually effective features from potentially useful ones is not obvious. In addition, the selection should be done simultaneously with the optimization of the dialog policy. In this paper, we propose an incremental feature selection method for the optimization of a dialog policy by RL, in which improvement of the dialog policy and the feature selection are conducted simultaneously. Experiments in dialog policy optimization by RL with a user simulator demonstrated the following: 1) that the proposed method can find a better dialog policy with fewer policy iterations and 2) the learning speed is comparable with the case where feature selection is conducted in advance.