# Numerical Methods for Mean-Field-Type Optimal Control Problems

arXiv: https://arxiv.org/abs/1703.10001 · HTML: https://mlsanity.com/paper/1703.10001/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2017.

## Built on by (most cited first, 4 of 4)

- [Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint](https://mlsanity.com/paper/2106.03787/) (2021)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [Stochastic Control Methods for Optimization](https://mlsanity.com/paper/2601.01248/) (2026)
- [Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type](https://mlsanity.com/paper/2210.00874/) (2022)

## Abstract (arXiv)

In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal condition obtained by linearizing the cost function. The terminal condition is updated by solving a Fokker-Planck equation. The first method can be seen as a gradient method and uses in an essential manner the convexity of the set of probability distributions. A convergence result for this method is provided. The second method incorporates a penalization term and provides feedback controls. We test the methods on four academic examples.