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

arXiv: https://arxiv.org/abs/2212.11518 · HTML: https://mlsanity.com/paper/2212.11518/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 22 Dec 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [An overview on deep learning-based approximation methods for partial differential equations](https://mlsanity.com/paper/2012.12348/) (2020)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Machine Learning for semi linear PDEs](https://mlsanity.com/paper/1809.07609/) (2018)
- [Neural networks-based algorithms for stochastic control and PDEs in finance](https://mlsanity.com/paper/2101.08068/) (2021)
- [Deep Learning Methods for Mean Field Control Problems with Delay](https://mlsanity.com/paper/1905.00358/) (2019)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Approximation error analysis of some deep backward schemes for nonlinear PDEs](https://mlsanity.com/paper/2006.01496/) (2020)
- [Numerical resolution of McKean-Vlasov FBSDEs using neural networks](https://mlsanity.com/paper/1909.12678/) (2019)
- [Mean-field neural networks: learning mappings on Wasserstein space](https://mlsanity.com/paper/2210.15179/) (2022)
- [Convergence of a robust deep FBSDE method for stochastic control](https://mlsanity.com/paper/2201.06854/) (2022)
- [A fast iterative PDE-based algorithm for feedback controls of nonsmooth mean-field control problems](https://mlsanity.com/paper/2108.06740/) (2021)
- [Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *](https://mlsanity.com/paper/1610.06805/) (2016)
- [Numerical Methods for Mean-Field-Type Optimal Control Problems](https://mlsanity.com/paper/1703.10001/) (2017)
- [Reservoir optimization and Machine Learning methods](https://mlsanity.com/paper/2106.08097/) (2021)
- [A Dynamic Game Model of Collective Choice in Multi-Agent Systems](https://mlsanity.com/paper/1506.09210/) (2015)

## Built on by (most cited first, 10 of 10)

- [Actor-Critic learning for mean-field control in continuous time](https://mlsanity.com/paper/2303.06993/) (2023)
- [Entropy annealing for policy mirror descent in continuous time and space](https://mlsanity.com/paper/2405.20250/) (2024)
- [Actor critic learning algorithms for mean-field control with moment neural networks](https://mlsanity.com/paper/2309.04317/) (2023)
- [Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms](https://mlsanity.com/paper/2604.27378/) (2026)
- [Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies](https://mlsanity.com/paper/2507.06428/) (2025)
- [Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems](https://mlsanity.com/paper/2603.21683/) (2026)
- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [Quantile and moment neural networks for learning functionals of distributions](https://mlsanity.com/paper/2303.11060/) (2023)
- [Consensus Based Stochastic Control](https://mlsanity.com/paper/2501.17801/) (2025)
- [Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach](https://mlsanity.com/paper/2605.08928/) (2026)

## 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.