Abstract
This paper shows that more consensus is not always beneficial to the convergence rate of consensus-based distributed computational algorithms. Specifically, we focus on the consensus-based distributed algorithm for solving linear equations, which aims to enable multiple agents in a network to cooperatively find a solution to large-scale linear equations. Such algorithms have two key components: local computation that happens within each agent; and global consensus that happens among connected agents through the networks. Intuitively, one expects more consensus in each iteration should speed up the convergence of such algorithms. However, according to the theoretical analysis and numerical simulations provided in this paper, such assumption does not hold. Counter-intuitively, we show that more consensus is not always beneficial to consensus-based distributed algorithms, and sometimes slow down the convergence.
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