Learning methods based on dynamic programming (DP) are receiving increasing attention in arti cial intelligence. Researchers have argued that DP provides the appropriate basis for compiling planning results into reactive strategies for real-time control, as well as for learning such strategies when the system being controlled is incompletely known. We introduce an algorithm based on DP, which we call Real-Time DP (RTDP), by which an embedded system can improve its performance with experience. RTDP generalizes Korf's Learning-Real-Time-A* algorithm to problems involving uncertainty. We invoke results from the theory of asynchronous DP to prove that RTDP achieves optimal behavior in several di erent classes of problems. We also use the theory of asynchronous DP to illuminate aspects of other DP-based reinforcement learning methods such as Watkins' Q-Learning algorithm. A secondary aim of this article is to provide a bridge between AI research on real-time planning and learning and relevant concepts and algorithms from control theory. 1