COMMUNICATION-EFFICIENT WEIGHTED ADMM FOR DECENTRALIZED NETWORK OPTIMIZATION

In this paper, we propose a weighted alternating direction method of multipliers (ADMM) to solve the consensus optimization problem over a decentralized network. Compared with the conventional ADMM that is popular in decentralized network optimization, the weighted ADMM is able to tune its weight matrices for the purpose of reducing the communication cost spent in the optimization process. We first prove convergence and establish linear convergence rate of the weighted ADMM. Second, we maximize the derived convergence speed and obtain the best weight matrices on a given topology. Third, observing that exchanging information with all the neighbors is expensive, we maximize the convergence speed while limit the number of communication arcs. This strategy finds a subgraph within the underlying topology to fulfill the optimization task and leads to a favorable tradeoff between the number of iterations and the communication cost per iteration. Numerical experiments demonstrate advantages of the weighted ADMM over its conventional counterpart in expediting the convergence speed and reducing the communication cost.