Distributed Solvers for Network Linear Equations with Scalarized Compression
Lei Wang, Zihao Ren, Deming Yuan, Guodong Shi
TL;DR
This article presents a compressed consensus flow that relies only on such scalarized communication, and employs such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and proves their linear convergence properties under scalar node communications.
Abstract
Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results.