A Unifying System Theory Framework for Distributed Optimization and Games
Abstract
This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the decision variables (e.g., a global cost gradient or constraint) and introduce a distributed consensus-oriented scheme to asymptotically approximate the unavailable information at each agent. Then, we delineate the proper methodology for intertwining the identified building blocks, i.e., the optimization-oriented method and the consensus-oriented one. The key intuition is to interpret the obtained interconnection as a singularly perturbed system. We rely on this interpretation to provide sufficient conditions for the building blocks to be successfully connected into a distributed scheme exhibiting the convergence guarantees of the centralized algorithm. Finally, we show the potential of our approach by developing a new distributed scheme for constraint-coupled problems with a linear convergence rate.
Cite
@article{arxiv.2401.12623,
title = {A Unifying System Theory Framework for Distributed Optimization and Games},
author = {Guido Carnevale and Nicola Mimmo and Giuseppe Notarstefano},
journal= {arXiv preprint arXiv:2401.12623},
year = {2025}
}