# Finite state N-agent and mean field control problems

arXiv: https://arxiv.org/abs/2010.11569 · HTML: https://mlsanity.com/paper/2010.11569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

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

- [Convergence of the Deep Galerkin Method for Finite State Mean Field Control Problems](https://mlsanity.com/paper/2405.13346/) (2024)

## Abstract (arXiv)

We examine mean field control problems on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. In absence of any convexity assumption, we exploit this characterization to prove convergence, as N grows, of the value functions of the centralized N-agent optimal control problem to the limit mean field control problem value function, with a convergence rate of order 1/√N. Then, assuming convexity, we show that the limit value function is smooth and establish propagation of chaos, i.e. convergence of the N-agent optimal trajectory to the unique limiting optimal trajectory, with an explicit rate.