A Constraint-Preserving Neural Network Approach for Solving Mean-Field Games Equilibrium

• URL: http://arxiv.org/abs/2501.17450v2
• Date: Mon, 10 Mar 2025 14:42:09 GMT
• Title: A Constraint-Preserving Neural Network Approach for Solving Mean-Field Games Equilibrium
• Authors: Jinwei Liu, Lu Ren, Wang Yao, Xiao Zhang,
• Abstract summary: Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria.<n>This paper proposes the NF-MKV Net, a network approach that integrates neural networks to solve FBSDEs and their associated fixed-point formulations of MFG equilibria.
• Score: 6.168001746423872
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the NF-MKV Net, a neural network approach that integrates process-regularized normalizing flow (NF) with state-policy-connected time-series neural networks to solve MKV FBSDEs and their associated fixed-point formulations of MFG equilibria. The method first reformulates MFG equilibria as MKV FBSDEs, embedding density evolution into equation coefficients within a probabilistic framework. Neural networks are then employed to approximate value functions and their gradients. To enforce volumetric invariance and temporal continuity, NF architectures impose loss constraints on each density transfer function.

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