Learning Regularized Graphon Mean-Field Games with Unknown Graphons
This addresses a specific bottleneck in multi-agent reinforcement learning for large populations, but it is incremental as it builds on prior work by improving convergence rates and adding estimation capabilities.
The paper tackles the problem of learning Nash Equilibrium in Graphon Mean-Field Games when graphons are unknown, proposing algorithms that converge at a rate of O(T^{-1/3}) and reduce exploitability in simulations.
We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs when the graphons are unknown. Our contributions are threefold. First, we propose the Proximal Policy Optimization for GMFG (GMFG-PPO) algorithm and show that it converges at a rate of $O(T^{-1/3})$ after $T$ iterations with an estimation oracle, improving on a previous work by Xie et al. (ICML, 2021). Second, using kernel embedding of distributions, we design efficient algorithms to estimate the transition kernels, reward functions, and graphons from sampled agents. Convergence rates are then derived when the positions of the agents are either known or unknown. Results for the combination of the optimization algorithm GMFG-PPO and the estimation algorithm are then provided. These algorithms are the first specifically designed for learning graphons from sampled agents. Finally, the efficacy of the proposed algorithms are corroborated through simulations. These simulations demonstrate that learning the unknown graphons reduces the exploitability effectively.