Title: Communication Efficient Primal Dual Algorithm for Nonconvex Nonsmooth Distributed Optimization. Abstract: Decentralized optimization problems frequently appear in the large scale machine learning problem. However, few works work on the nonconvex nonsmooth case. In this paper, we give a primal-dual algorithm to solve the nonconvex nonsmooth optimization problem. In addition, to reduce communication overhead, we introduce compression function. We analyze the convergence results of the algorithm and shows the algorithm meets the lower iteration complexity bound. Besides, we conduct two experiments, both of them shows the efficacy of our algorithm. 