# McKean-Vlasov optimal control: the dynamic programming principle

arXiv: https://arxiv.org/abs/1907.08860 · HTML: https://mlsanity.com/paper/1907.08860/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Discrete-Time Mean Field Control with Environment States](https://mlsanity.com/paper/2104.14900/) (2021)
- [Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations](https://mlsanity.com/paper/2604.27372/) (2026)
- [Learning from one graph: transductive learning guarantees via the geometry of small random worlds](https://mlsanity.com/paper/2509.06894/) (2025)
- [Learning Mean-Field Control for Delayed Information Load Balancing in Large Queuing Systems](https://mlsanity.com/paper/2208.04777/) (2022)
- [Robust Q-learning for mean-field control under Wasserstein uncertainty in common noise](https://mlsanity.com/paper/2606.20356/) (2026)

## Abstract (arXiv)

We study the McKean-Vlasov optimal control problem with common noise in various formulations, namely the strong and weak formulation, as well as the Markovian and non-Markovian formulations, and allowing for the law of the control process to appear in the state dynamics. By interpreting the controls as probability measures on an appropriate canonical space with two filtrations, we then develop the classical measurable selection, conditioning and concatenation arguments in this new context, and establish the dynamic programming principle under general conditions.