Can sparse networks ensure Q-learning convergence in multi-agent systems?
Multi-Agent Q-Learning Dynamics in Random Networks: Convergence due to Exploration and Sparsity
This paper investigates how the structure of a network connecting multiple AI agents affects their ability to learn and cooperate effectively. Specifically, it examines Q-learning, a common reinforcement learning algorithm, within network polymatrix games, where agents interact strategically with their neighbors. The study finds that sparser networks, where agents interact with fewer others, lead to better convergence to stable solutions even with limited exploration, while densely connected networks may hinder convergence. This is relevant because the network structure can be controlled, potentially guaranteeing the feasibility of learning in multi-agent systems.
Key points for LLM-based multi-agent systems:
- Network sparsity promotes convergence: LLM agents interacting on sparser networks are more likely to achieve stable cooperative outcomes during Q-learning, even with lower exploration rates.
- Exploration-exploitation balance: The exploration rate, which governs how much agents explore new strategies versus exploiting learned ones, is crucial. Too much exploration can lead to random behavior, but too little prevents effective learning. The study provides theoretical bounds on appropriate exploration rates based on network sparsity and the similarity of agents' incentives (intensity of identical interests).
- Impact of network structure: The way LLM agents are connected (e.g., fully connected, ring network, community structure) significantly impacts their learning dynamics and the stability of the system.
- Controllable convergence: By controlling the network structure and exploration rates, developers can improve the likelihood of stable and effective outcomes in LLM-based multi-agent systems. This has practical implications for designing robust and predictable multi-agent applications.