Fast Incremental ADMM for Decentralized Consensus Multi-Agent Optimization

The alternating direction method of multipliers (ADMM) has been recently recognized as well-suited for solving distributed optimization problems among multiple agents. Nonetheless, there remains a scarcity of research exploring ADMM's communication costs. Especially for large-scale multi-agent systems, the impact of communication costs becomes more significant. On the other hand, it is well-known that the convergence property of ADMM is significantly influenced by the different parameters while tuning these parameters arbitrarily would disrupt the convergence of ADMM. To this end, inspired by the preliminary works on incremental ADMM, we propose a fast incremental ADMM algorithm that can solve large-scale multi-agent optimization problems with enhanced communication efficiency and fast convergence speed. The proposed algorithm can improve the convergence speed by introducing an extra adjustable parameter to modify the penalty parameter
$\rho$
in both primal and dual updates of incremental ADMM. With several mild assumptions, we provide the convergence analysis of our proposed algorithm. Finally, the numerical experiments demonstrate the superiority of the proposed fast incremental ADMM algorithm compared to the other incremental ADMM-type methods.