# Viscosity Solutions for McKean-Vlasov Control on a torus

arXiv: https://arxiv.org/abs/2212.11053 · HTML: https://mlsanity.com/paper/2212.11053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2022.

## Built on by (most cited first, 2 of 2)

- [Policy Gradient for Continuous-Time Mean-Field Control](https://mlsanity.com/paper/2605.20718/) (2026)
- [Functional role of synchronization: A mean-field control perspective](https://mlsanity.com/paper/2502.00590/) (2025)

## Abstract (arXiv)

An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a novel smooth Fourier Wasserstein metric. A comparison result between the Lipschitz viscosity sub and super solutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.