In this paper, we devise a communication-efficientdecentralized algorithm, named as communication-censoredADMM (COCA), to solve a convex consensus optimization problem defined over a network. Similar to popular decentralizedconsensus optimization algorithms such as ADMM (abbreviatedfor the alternating direction method of multipliers), at everyiteration of COCA, a node exchanges its local variable withneighbors, and then updates its local variable according tothe received neighboring variables and its local cost function.A different feature of COCA is that a node is not allowedto transmit its local variable to neighbors, if this variable isnot sufficiently different to the previously transmitted one. Thesufficiency of the difference is evaluated by a properly designedcensoring function. Though this censoring strategy may slowdown the optimization process, it effectively reduces the communication cost. We prove that when the censoring function isproperly chosen, COCA converges to an optimal solution of theconvex consensus optimization problem. Further, if the localcost functions are strongly convex, COCA has a fast linearconvergence rate. Numerical experiments demonstrate that,given a target solution accuracy, COCA is able to significantlyreduce the overall communication cost compared to existingalgorithms including ADMM, and hence fits for applicationswhere network communication is a bottleneck.
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