# Extended Mean Field Control Problems: stochastic maximum principle and transport perspective

arXiv: https://arxiv.org/abs/1802.05754 · HTML: https://mlsanity.com/paper/1802.05754/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Indexability is Not Enough for Whittle: Improved, Near-Optimal Algorithms for Restless Bandits](https://mlsanity.com/paper/2211.00112/) (2022)
- [Conditional COT-GAN for Video Prediction with Kernel Smoothing](https://mlsanity.com/paper/2106.05658/) (2021)
- [Fitted value iteration methods for bicausal optimal transport](https://mlsanity.com/paper/2306.12658/) (2023)
- [Convergence of Proximal Policy Gradient Method for Problems with Control Dependent Diffusion Coefficients](https://mlsanity.com/paper/2505.18379/) (2025)
- [Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies](https://mlsanity.com/paper/2607.11005/) (2026)

## Abstract (arXiv)

We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufficient form, which extend the known conditions to this general framework. Furthermore, we suggest a variational approach to study a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.