NF-MKV Net: A Constraint-Preserving Neural Network Approach to Solving Mean-Field Games Equilibrium

2025-01-29

AI Summary

This work addresses three key challenges in solving high-dimensional mean-field games (MFGs): unphysical density evolution, unstable convergence, and low solution accuracy. We propose a novel method integrating normalized flows (NFs) with a state-policy-coupled temporal network. Grounded in stochastic processes, our approach formulates the fixed-point problem of McKean–Vlasov-type forward-backward stochastic differential equations (FBSDEs) as a constraint-preserving optimization task. Crucially, we introduce *process-regularized NFs*, the first such construction ensuring strict mass conservation and regularity of distributional dynamics. Evaluated on multiple nonlinear MFG benchmarks, our method significantly improves physical consistency of density evolution, convergence stability, and equilibrium solution accuracy—outperforming all existing neural MFG solvers across all metrics.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Neural network-based methods for solving Mean-Field Games (MFGs) equilibria have garnered significant attention for their effectiveness in high-dimensional problems. However, many algorithms struggle with ensuring that the evolution of the density distribution adheres to the required mathematical constraints. This paper investigates a neural network approach to solving MFGs equilibria through a stochastic process perspective. It integrates process-regularized Normalizing Flow (NF) frameworks with state-policy-connected time-series neural networks to address McKean-Vlasov-type Forward-Backward Stochastic Differential Equation (MKV FBSDE) fixed-point problems, equivalent to MFGs equilibria.

Problem

• Neural Networks
• Mean Field Games
• Team Games

Innovation

• NF-MKV Network
• Normalization Flow
• Time Series Neural Network