mlsanityData to 14 Oct 2026

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

arXiv 2002.10113 ↗First posted 24 Feb 2020cs.LG cs.MA math.OCcited by 35

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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.

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

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Citing papers per year: 2021: 2; 2022: 8; 2023: 5; 2024: 4; 2025: 10; 2026: 6.

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  1. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 101
  2. 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 86
  3. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 50
  4. 2022Deep Generalized Schr"odinger Bridgecited by 47
  5. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  6. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 31
  7. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 24
  8. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  9. 2022Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularizationcited by 17
  10. 2022Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Schemecited by 17
  11. 2022Mean-field neural networks: learning mappings on Wasserstein spacecited by 16
  12. 2022Explainable AI via Learning to Optimizecited by 14
23 more
  1. 2021DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle methodcited by 9
  2. 2022Provably convergent quasistatic dynamics for mean-field two-player zero-sum gamescited by 9
  3. 2022Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimizationcited by 9
  4. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problemscited by 7
  5. 2024Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizationscited by 3
  6. 2025End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagationcited by 3
  7. 2025High-dimensional Mean-Field Games by Particle-based Flow Matchingcited by 3
  8. 2023Decoding Mean Field Games from Population and Environment Observations By Gaussian Processescited by 2
  9. 2025Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problemscited by 2
  10. 2025A Constraint-Preserving Neural Network Approach for Solving Mean-Field Games Equilibriumcited by 1
  11. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  12. 2026On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonianscited by 1
  13. 2026Kernel-based potential mean-field games with unbiased random Fourier U-statisticscited by 1
  14. 2023Reimagining Demand-Side Management with Mean Field Learningcited by 0
  15. 2025PIONM: A Generalized Approach to Solving Density-Constrained Mean-Field Games Equilibrium under Modified Boundary Conditionscited by 0
  16. 2025Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equationscited by 0
  17. 2025Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problemscited by 0
  18. 2025Exact Solutions to the Quantum Schr"odinger Bridge Problemcited by 0
  19. 2025Multi-Marginal Schr"odinger Bridge Matchingcited by 0
  20. 2026Taming Epilepsy: Mean Field Control of Whole-Brain Dynamicscited by 0
  21. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0
  22. 2026End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layerscited by 0
  23. 2026Self-supervised In-context Operator Learning for Stochastic Mean-Field Controlcited by 0