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We consider the problem of intelligent and efficient resource management framework in mobile edge computing (MEC), which can reduce delay and energy consumption, featuring distributed optimization and efficient congestion avoidance mechanism. In this paper, we present a Cooperative Learning framework for resource management in MEC from an Alternating Direction Method of Multipliers (ADMM) perspective, called CL-ADMM framework. First, in order to caching task efficiently in a group, a novel task popularity estimating scheme is proposed, which is based on semi-Markov process model, then a greedy task cooperative caching mechanism has been established, which can effectively reduce delay and energy consumption. Secondly, for addressing group congestion, a dynamic task migration scheme based on cooperative improved Q-learning is proposed, which can effectively reduce delay and alleviate congestion. Thirdly, for minimizing delay and energy consumption for resources allocation in a group, we formulate it as an optimization problem with a large number of variables, and then exploit a novel ADMM based scheme to address this problem, which can reduce the complexity of problem with a new set of auxiliary variables, these sub-problems are all convex problems, and can be solved by using a primal-dual approach, guaranteeing its convergences. Then we prove that the convergence by using Lyapunov theory. Numerical results demonstrate the effectiveness of the CL-ADMM and it can effectively reduce delay and energy consumption for MEC.