# Mean-field optimal control as Gamma-limit of finite agent controls

arXiv: https://arxiv.org/abs/1803.04689 · HTML: https://mlsanity.com/paper/1803.04689/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2018.

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

- [On kernel-based statistical learning in the mean field limit](https://mlsanity.com/paper/2310.18074/) (2023)
- [Data/moment-driven approaches for fast predictive control of collective dynamics](https://mlsanity.com/paper/2402.15611/) (2024)
- [Maximum Principle of Optimal Probability Density Control](https://mlsanity.com/paper/2505.18362/) (2025)
- [Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics](https://mlsanity.com/paper/2603.18035/) (2026)

## Abstract (arXiv)

This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a Gamma-convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.