Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction determined by the mixing rate of the underlying network topology. For very sparse graphs this can yield a bottleneck, slowing down the convergence of the learning algorithm. We show that a sequence of matrices achieving finite-time consensus can be learned for unknown graph topologies in a decentralized manner by solving a constrained matrix factorization problem. We demonstrate numerically the benefit of the resulting scheme in both structured and unstructured graphs.
@article{arxiv.2404.07018,
title = {Learned Finite-Time Consensus for Distributed Optimization},
author = {Aaron Fainman and Stefan Vlaski},
journal= {arXiv preprint arXiv:2404.07018},
year = {2024}
}