Can graphons model open multi-agent consensus?
Consensus on Open Multi-Agent Systems Over Graphs Sampled from Graphons
This paper explores how to use graphons to model and analyze open multi-agent systems for linear consensus, where agents can join or leave the system. Specifically, it examines how the connections between agents, represented by graphs sampled from graphons, affect the system's ability to reach agreement (consensus). It derives performance bounds, showing how disagreement among agents is influenced by arrival/departure rates, the graph structure, and the spectrum of the Laplacian matrix (related to network connectivity).
For LLM-based multi-agent systems, the key takeaway is the use of graphons to model evolving connection topologies within the system. This addresses the challenge of dynamic agent interactions, where the set of agents and their relationships are not fixed. The paper also provides a way to calculate bounds on consensus performance, which is crucial for understanding and designing robust, efficient multi-agent applications using LLMs. This is especially relevant for large systems, where analyzing all possible interaction combinations is computationally infeasible, as the paper simplifies the computational burden for stochastic block model graphons.