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Numerical resolution of McKean-Vlasov FBSDEs using neural networks

arXiv 1909.12678 ↗First posted 27 Sep 2019math.OCcited by 19

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Abstract (arXiv)

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean field games and mean field control problems in moderate dimension. We analyze the numerical behavior of our algorithms on several examples including non linear quadratic models.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Sep 2019.

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Citing papers per year: 2021: 3; 2022: 3; 2023: 4; 2024: 4; 2025: 3; 2026: 2.

19 papers.

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  1. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  2. 2021Scaling up Mean Field Games with Online Mirror Descentcited by 29
  3. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  4. 2023Actor-Critic learning for mean-field control in continuous timecited by 19
  5. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 14
  6. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  7. 2022Mean-field neural networks-based algorithms for McKean-Vlasov control problems *cited by 9
  8. 2023Actor critic learning algorithms for mean-field control with moment neural networkscited by 6
  9. 2024Deep Backward and Galerkin Methods for the Finite State Master Equationcited by 6
  10. 2025Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operatorscited by 3
  11. 2025Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Gamescited by 2
  12. 2023Deep Learning for Mean Field Optimal Transportcited by 1
7 more
  1. 2024Learning to Stop: Deep Learning for Mean Field Optimal Stoppingcited by 1
  2. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  3. 2024A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agentscited by 0
  4. 2024Mean-field Chaos Diffusion Modelscited by 0
  5. 2025Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noisecited by 0
  6. 2026Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approachcited by 0
  7. 2026A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatchcited by 0