Consensus-based Distributed Discrete Optimal Transport for Decentralized Resource Matching

TL;DR

This paper introduces a decentralized, consensus-based algorithm for solving large-scale discrete optimal transport problems, enhancing efficiency, privacy, and adaptability in resource matching.

Contribution

It develops fully distributed primal and dual algorithms using ADMM, proving their equivalence and convergence, and demonstrates their practical effectiveness through numerical experiments.

Findings

Algorithms guarantee efficiency and privacy in resource matching.

Primal and dual algorithms are proven equivalent and convergent.

Numerical experiments confirm online adaptability and bargaining insights.

Abstract

Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale problems. In this paper, we take a consensus-based approach to decentralize discrete optimal transport problems and develop fully distributed algorithms with alternating direction method of multipliers. We show that our algorithms guarantee certain levels of efficiency and privacy besides the distributed nature. We further derive primal and dual algorithms by exploring the primal and dual problems of discrete optimal transport with linear utility functions and prove the equivalence between them. We verify the convergence, online adaptability, and the equivalence between the primal algorithm and the dual algorithm with numerical experiments. Our algorithms reflect the bargaining between sources and targets on the amounts and prices of transferred resources and reveal an averaging principle which can be used to regulate resource markets and improve resource efficiency.