This paper proposes an improved cross-layer control mechanism to efficiently stream videos to mobile users over an LTE network. A proxy-based filtering algorithm among scalable layers is considered to decide the number of SVC layers to transmit for each frame according to the communication conditions and to the class to which the video belongs to. The problem is cast in the context of Markov Decision Processes which allow the design of foresighted policies maximizing some long-term accumulated reward. Optimal actions to apply to the system are obtained by reinforcement learning. The proposed solution is implemented in an LTE simulation platform. Experiments show the performance of the proposed class-based layer filtering algorithm for a single video transmission and its robustness to content changes.