# Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games

arXiv: https://arxiv.org/abs/2002.10113 · HTML: https://mlsanity.com/paper/2002.10113/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 30 of 35)

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- [Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems](https://mlsanity.com/paper/2502.11506/) (2025)
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- [On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians](https://mlsanity.com/paper/2602.00921/) (2026)
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- [Reimagining Demand-Side Management with Mean Field Learning](https://mlsanity.com/paper/2302.08190/) (2023)
- [PIONM: A Generalized Approach to Solving Density-Constrained Mean-Field Games Equilibrium under Modified Boundary Conditions](https://mlsanity.com/paper/2504.03209/) (2025)
- [Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2504.13228/) (2025)
- [Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems](https://mlsanity.com/paper/2505.00909/) (2025)
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## Abstract (arXiv)

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems.