mlsanityData to 7 Oct 2026

Mean-field neural networks-based algorithms for McKean-Vlasov control problems *

arXiv 2212.11518 ↗First posted 22 Dec 2022math.OC q-fin.CP stat.MLcited by 9

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Abstract (arXiv)

This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose several algorithms either based on dynamic programming with control learning by policy or value iteration, or backward SDE from stochastic maximum principle with global or local loss functions. Extensive numerical results on different examples are presented to illustrate the accuracy of each of our eight algorithms. We discuss and compare the pros and cons of all the tested methods.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 19 of its 34 references that are in the map. First posted on arXiv 22 Dec 2022.

Builds on

19 of 34 references.

References · 19

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7 more
  1. 2022Mean-field neural networks: learning mappings on Wasserstein spacecited by 15
  2. 2022Convergence of a robust deep FBSDE method for stochastic controlcited by 11
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 1; 2026: 4.

9 papers.

  1. 2023Actor-Critic learning for mean-field control in continuous timecited by 19
  2. 2024Entropy annealing for policy mirror descent in continuous time and spacecited by 9
  3. 2023Actor critic learning algorithms for mean-field control with moment neural networkscited by 6
  4. 2025Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studiescited by 3
  5. 2026Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systemscited by 3
  6. 2026Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithmscited by 3
  7. 2026Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Controlcited by 2
  8. 2023Quantile and moment neural networks for learning functionals of distributionscited by 1
  9. 2026Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approachcited by 0