A Distributed Bilevel Framework for the Macroscopic Optimization of Multi-Agent Systems

TL;DR

This paper introduces a distributed bilevel optimization algorithm for large-scale multi-agent systems, enabling agents to collaboratively optimize emergent macroscopic behavior through local estimation and updates.

Contribution

It presents a novel distributed bilevel framework that combines local macroscopic state estimation with hypergradient-based microscopic updates for system-wide optimization.

Findings

Convergence to stationary points is theoretically proven.

Numerical simulations demonstrate the method's effectiveness.

The approach effectively guides multi-agent systems toward desired macroscopic behaviors.

Abstract

In this paper, we propose a novel distributed algorithm to optimize the emergent macroscopic behavior of large-scale multi-agent systems via microscopic actions. We cast this task as a bilevel optimization problem, where the upper level formalizes the desired macroscopic target behavior through a suitable performance criterion, which is shaped in the lower level by leveraging a compressed aggregate representation estimating the macroscopic state. More precisely, the macroscopic state is parametrized by an exponential-family of distributions and constructed from the multi-agent microscopic configuration. The proposed algorithm integrates a distributed estimation mechanism, through which each agent reconstructs the macroscopic state locally, with a hypergradient-based update of the microscopic states aimed at improving the collective macroscopic behavior. We prove convergence to the set of stationary points of the bilevel problem via timescale separation arguments. Numerical simulations validate the effectiveness of the proposed method.