# Deep Learning for Population-Dependent Controls in Mean Field Control Problems with Common Noise

arXiv: https://arxiv.org/abs/2306.04788 · HTML: https://mlsanity.com/paper/2306.04788/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2023.

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

- [Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behavior](https://mlsanity.com/paper/2307.06175/) (2023)
- [Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems](https://mlsanity.com/paper/2409.16471/) (2024)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [Nonlocal Mean Field Schr"odinger Bridge with Learned Interactions](https://mlsanity.com/paper/2606.04265/) (2026)

## Abstract (arXiv)

In this paper, we propose several approaches to learn the optimal population-dependent controls in order to solve mean field control problems (MFC). Such policies enable us to solve MFC problems with forms of common noises at a level of generality that was not covered by existing methods. We analyze rigorously the theoretical convergence of the proposed approximation algorithms. Of particular interest for its simplicity of implementation is the N-particle approximation. The effectiveness and the flexibility of our algorithms is supported by numerical experiments comparing several combinations of distribution approximation techniques and neural network architectures. We use three different benchmark problems from the literature: a systemic risk model, a price impact model, and a crowd motion model. We first show that our proposed algorithms converge to the correct solution in an explicitly solvable MFC problem. Then, we show that population-dependent controls outperform state-dependent controls. Along the way, we show that specific neural network architectures can improve the learning further.