# Mean-field control of non exchangeable systems

arXiv: https://arxiv.org/abs/2407.18635 · HTML: https://mlsanity.com/paper/2407.18635/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2024.

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

- [Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems](https://mlsanity.com/paper/2603.21683/) (2026)

## Abstract (arXiv)

We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability laws. We prove the well-posedness of such systems and define the control problem together with its related value function. We next prove a law invariance property for the value function which allows us to work on the set of collections of probability laws. We show that the value function satisfies a dynamic programming principle (DPP) on the flow of collections of probability measures. We also derive a chain rule for a class of regular functions along the flows of collections of marginal laws of diffusion processes. Combining the DPP and the chain rule, we prove that the value function is a viscosity solution of a Bellman dynamic programming equation in a L2-set of Wasserstein space-valued functions.