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The increase of Internet application requirements, such as throughput and delay, has spurred the need for transport protocols with flexible transmission control. Current TCP congestion control adopts an Additive Increase Multiplicative Decrease (AIMD) algorithm that linearly increases or exponentially decreases the congestion window based on transmission acknowledgments. In this paper, we propose an AIMD-like media-aware congestion control that determines the optimal congestion window updating policy for multimedia transmission. The media-aware congestion control problem is formulated as a Partially Observable Markov Decision Process (POMDP), which maximizes the long-term expected quality of the received multimedia application. The solution of this POMDP problem gives a policy adapted to multimedia applications' characteristics (i.e., distortion impacts and delay deadlines of multimedia packets). Note that to obtain the optimal congestion policy, the sender requires the complete statistical knowledge of both multimedia traffic and the network environment, which may not be available in practice. Hence, an online reinforcement learning in the POMDP-based solution provides a powerful tool to accurately estimate the environment and to adapt the source to network variations on the fly. Simulation results show that the proposed online learning approach can significantly improve the received video quality while maintaining the responsiveness and TCP-friendliness of the congestion control in various network scenarios.