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Future wireless networks are designed to support adaptive multimedia by controlling individual ongoing flows to increase or decrease their bandwidths in response to changes in traffic load. There is growing interest in quality-of-service (QoS) provisioning under this adaptive multimedia framework, in which a bandwidth adaptation algorithm needs to be used in conjunction with the call admission control algorithm. This paper presents a novel method for QoS provisioning via average reward reinforcement learning in conjunction with stochastic approximation, which can maximize the network revenue subject to several predetermined QoS constraints. Unlike other model-based algorithms (e.g., linear programming), our scheme does not require explicit state transition probabilities, and therefore, the assumptions behind the underlying system model are more realistic than those in previous schemes. In addition, when we consider the status of neighboring cells, the proposed scheme can dynamically adapt to changes in traffic condition. Moreover, the algorithm can control the bandwidth adaptation frequency effectively by accounting for the cost of bandwidth switching in the model. The effectiveness of the proposed approach is demonstrated using simulation results in adaptive multimedia wireless networks.