On Local Computation for Network-Structured Convex Optimization in Multiagent Systems

A number of prototypical optimization problems in multiagent systems (e.g., task allocation and network load-sharing) exhibit a highly local structure, that is, each agent’s decision variables are only directly coupled to few other agent’s variables through the objective function or the constraints. In this article, we develop a rigorous notion of “locality” that quantifies the degree to which agents can compute their portion of the global solution of such a distributed optimization problem based solely on information in their local neighborhood. We build upon the results of Rebeschini and Tatikonda to develop a more general theory of locality that fully captures the importance of problem data to individual solution components, as opposed to a theory that only captures response to perturbations. This analysis provides a theoretical basis for a rather simple algorithm in which agents individually solve a truncated subproblem of the global problem, where the size of the subproblem used depends on the locality of the problem, and the desired accuracy. Numerical results show that the proposed theoretical bounds are remarkably tight for well-conditioned problems.