2023/10/12 by Fengzhuo Zhang, Vincent Y. F. Tan, Zhang, Fengzhuo +5 · 3 citations
Decision Sciences · #Advanced Bandit Algorithms Research #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Electrical engineering #Game Theory and Applications #Machine Learning (stat.ML) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2310.08089
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies two fundamental problems in regularized Graphon Mean-Field Games (GMFGs). First, we establish the existence of a Nash Equilibrium (NE) of any λ-regularized GMFG (for λ≥ 0). This result relies on weaker conditions than those in previous works for analyzing both unregularized GMFGs (λ=0) and λ-regularized MFGs, which are special cases of GMFGs. Second, we propose provably efficient algorithms to learn the NE in weakly monotone GMFGs, motivated by Lasry and Lions [2007]. Previous literature either only analyzed continuous-time algorithms or required extra conditions to analyze discrete-time algorithms. In contrast, we design a discrete-time algorithm and derive its convergence rate solely under weakly monotone conditions. Furthermore, we develop and analyze the action-value function estimation procedure during the online learning process, which is absent from algorithms for monotone GMFGs. This serves as a sub-module in our optimization algorithm. The efficiency of the designed algorithm is corroborated by empirical evaluations.