Abstract
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.
| Original language | English (US) |
|---|---|
| Journal | Advances in Neural Information Processing Systems |
| Volume | 36 |
| State | Published - 2023 |
| Event | 37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States Duration: Dec 10 2023 → Dec 16 2023 |
Funding
Fengzhuo Zhang and Vincent Tan acknowledge funding by the Singapore Data Science Consortium (SDSC) Dissertation Research Fellowship, the Singapore Ministry of Education Academic Research Fund (AcRF) Tier 2 under grant number A-8000423-00-00, and AcRF Tier 1 under grant numbers A-8000980-00-00 and A-8000189-01-00. Zhaoran Wang acknowledges National Science Foundation (Awards 2048075, 2008827, 2015568, 1934931), Simons Institute (Theory of Reinforcement Learning), Amazon, J.P. Morgan, and Two Sigma for their support.
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing