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

• URL: http://arxiv.org/abs/2501.17450v1
• Date: Wed, 29 Jan 2025 07:14:09 GMT
• Title: NF-MKV Net: A Constraint-Preserving Neural Network Approach to Solving Mean-Field Games Equilibrium
• Authors: Jinwei Liu, Lu Ren, Wang Yao, Xiao Zhang,
• Abstract summary: This paper investigates a neural network approach to solving MFGs equilibria through a process perspective. It integrates state-policy-connected time-series neural networks to address McKean-Vlasov-type Forward-Backward Differential Equation (MKVDE) fixed-point problems.
• Score: 6.168001746423872
• License:
• 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.

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