Work

On Graphs with Finite-Time Consensus and Their Use in Gradient Tracking

Year: 2025

Type: article

Abstract: . This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in the decentralized optimization algorithm Gradient Tracking. For each of the studied graph sequences, we provide an explicit weight matrix representation and prove their finite-time consensus property. Moreover, we incorporate such topology sequences into Gradient Tracking and present a new algorithmic scheme called Gradient Tracking for Finite-Time Consensus Topologies (GT-FT). We analyze the new scheme for nonconvex problems with stochastic gradient estimates. Our analysis shows that the convergence rate of GT-FT does not depend on the heterogeneity of the agents’ functions or the connectivity of any individual graph in the topology sequence. Furthermore, owing to the sparsity of the graphs, GT-FT requires lower communication costs than Gradient Tracking using the static counterpart of the topology sequence.

Source: SIAM Journal on Optimization

DOI: 10.1137/24m1661455

Authors: Edward Duc Hien Nguyen, Xin Jiang, Bicheng Ying, César A. Uribe

Institutions: Rice University, Lehigh University, Cornell University, Google (United States)

Language: English

Topic: Distributed Control Multi-Agent Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: Enabling Next-Generation Decentralized Learning: Structure, Models, and Methods, SHF: Medium:DILSE: Codesigning Decentralized Incremental Learning System via Streaming Data Summarization on Edge