A Unifying System Theory Framework for Distributed Optimization and Games

2024/01/23 by Carnevale, Guido, Mimmo, Nicola, Notarstefano, Giuseppe · 3 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2401.12623

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.

Cited by

• Convergence Analysis of Distributed Optimization: A Dissipativity Framework
• Policy Gradient with Self-Attention for Model-Free Distributed Nonlinear Multi-Agent Games
• Control-Based Online Distributed Optimization

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