# An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics

arXiv: https://arxiv.org/abs/2203.14554 · HTML: https://mlsanity.com/paper/2203.14554/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)

## Abstract (arXiv)

We establish an algebraic rate of convergence in the large number of players limit of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem also known as mean field control. The rate is obtained in the presence of both idiosyncratic and common noises and in a setting where the value function for the McKean-Vlasov problem need not be smooth. Our approach relies crucially on uniform in N Lipschitz and semi-concavity estimates for the N-particle value functions as well as a certain concentration inequality.