Learning Mean Field Control on Sparse Graphs

TL;DR

This paper introduces a new mean field control model for sparse agent networks, providing scalable algorithms that outperform existing methods on synthetic and real-world networks, addressing a key challenge in multi-agent reinforcement learning.

Contribution

The paper proposes a novel mean field control framework for sparse graphs, extending existing models to include power law networks and designing scalable algorithms for such structures.

Findings

Outperforms existing methods on synthetic networks

Effective on real-world power law networks

Scalable algorithms for sparse graph sequences

Abstract

Large agent networks are abundant in applications and nature and pose difficult challenges in the field of multi-agent reinforcement learning (MARL) due to their computational and theoretical complexity. While graphon mean field games and their extensions provide efficient learning algorithms for dense and moderately sparse agent networks, the case of realistic sparser graphs remains largely unsolved. Thus, we propose a novel mean field control model inspired by local weak convergence to include sparse graphs such as power law networks with coefficients above two. Besides a theoretical analysis, we design scalable learning algorithms which apply to the challenging class of graph sequences with finite first moment. We compare our model and algorithms for various examples on synthetic and real world networks with mean field algorithms based on Lp graphons and graphexes. As it turns out, our approach outperforms existing methods in many examples and on various networks due to the special design aiming at an important, but so far hard to solve class of MARL problems.