# Discrete time McKean-Vlasov control problem: a dynamic programming approach

arXiv: https://arxiv.org/abs/1511.09273 · HTML: https://mlsanity.com/paper/1511.09273/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2015.

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

- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [An Optimal Control Approach To Transformer Training](https://mlsanity.com/paper/2603.09571/) (2026)
- [MESOB: Balancing Equilibria & Social Optimality](https://mlsanity.com/paper/2307.07911/) (2023)
- [Robust Q-learning for mean-field control under Wasserstein uncertainty in common noise](https://mlsanity.com/paper/2606.20356/) (2026)

## Abstract (arXiv)

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean-Vlasov control problem.