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For ultra-dense networks with wireless backhaul, caching strategy at small base stations (SBSs), usually with limited storage, is critical to meet massive high data rate requests. Since the content popularity profile varies with time in an unknown way, we exploit reinforcement learning (RL) to design a cooperative caching strategy with maximum-distance separable (MDS) coding. We model the MDS coding based cooperative caching as a Markov decision process to capture the popularity dynamics and maximize the long-term expected cumulative traffic load served directly by the SBSs without accessing the macro base station. For the formulated problem, we first find the optimal solution for a small-scale system by embedding the cooperative MDS coding into Q-learning. To cope with the large-scale case, we approximate the state-action value function heuristically. The approximated function includes only a small number of learnable parameters and enables us to propose a fast and efficient action-selection approach, which dramatically reduces the complexity. Numerical results verify the optimality/near-optimality of the proposed RL based algorithms and show the superiority compared with the baseline schemes. They also exhibit good robustness to different environments.