Vector-Valued Gossip over w-Holonomic Networks

Erkan Bayram, Mohamed-Ali Belabbas, Tamer Başar
11/8/2023
math.OCcs.MA

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Abstract

We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "$w$-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.

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Cite this paper

@article{bayram2023vectorvalued,
  title  = {Vector-Valued Gossip over w-Holonomic Networks},
  author = {Erkan Bayram and Mohamed-Ali Belabbas and Tamer Başar},
  year   = {2023},
  eprint = {2311.04455},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2311.04455v1}
}

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