Research in reinforcementlearning (RL)has thus far concentrated on two optimality criteria: the discounted framework, which has been very well-studied, and the averagereward framework, in which interest is rapidly increasing. In this paper, we present a framework called sensitive discount optimality which o ers an elegant way of linking these two paradigms. Although sensitive discount optimality has been well studied in dynamic programming, with several provably convergent algorithms, it has not received any attention in RL. This framework is based on studying the propertiesof the expected