In a spontaneous spoken dialogue understanding system, real-time response and robustness to the environment are required. To realize these requirements, we adopted a multi-agent system architecture. In this paper, we propose a reinforcement learning method for a phoneme recognizing agent as a sample agent, and adopt a continuous dynamic programming technique to deal with continuous phoneme recognition. To clarify the fundamental characteristics of the proposed method, we define some simple quasi conditions for the experiments, and confirm favorable results. The system can be expected to achieve high adaptability to the environment (e.g., variation of speakers and tasks) and robustness.