Two-Facet Scalable Cooperative Optimization of Multi-Agent Systems in The Networked Environment

TL;DR

This paper introduces a novel two-facet scalable decentralized optimization framework for large-scale multi-agent systems, effectively reducing network complexity and enabling efficient, communication-free optimization in networked environments.

Contribution

It develops a systemic network dimension reduction technique and a shrunken-primal-multi-dual subgradient algorithm, advancing scalability and decentralization in multi-agent optimization.

Findings

The framework achieves scalability with large agent populations and network dimensions.

It requires no agent-to-agent communication or additional aggregators.

Demonstrated effectiveness in electric vehicle charging and traffic congestion control simulations.

Abstract

Cooperatively optimizing a vast number of agents that are connected over a large-scale network brings unprecedented scalability challenges. This paper revolves around problems optimizing coupled objective functions under coupled network-induced constraints and local constraints. The scalability of existing optimization paradigms is limited by either the agent population size or the network dimension. As a radical improvement, this paper for the first time constructs a two-facet scalable decentralized optimization framework. To this end, we first develop a systemic network dimension reduction technique to virtually cluster the agents and lower the dimension of network-induced constraints, then constitute a novel shrunken-primal-multi-dual subgradient (SPMDS) algorithm based on the reduced-dimension network. Rigorous optimality and convergence analyses of the proposed decentralized optimization framework are provided. The SPMDS-based optimization framework is free of agent-to-agent communication and no additional aggregators are required for agent clusters. The efficiency and efficacy of the proposed approaches are demonstrated, in comparison with benchmark methods, through simulations of electric vehicle charging control problems and traffic congestion control problems.