Viscosity Solutions for McKean-Vlasov Control on a torus
Optimization and Control
2022-12-29 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2212.11053,
title = {Viscosity Solutions for McKean-Vlasov Control on a torus},
author = {H. Mete Soner and Qinxin Yan},
journal= {arXiv preprint arXiv:2212.11053},
year = {2022}
}
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21 pages