Extended Mean Field Control Problems: stochastic maximum principle and transport perspective
Optimization and Control
2018-06-26 v2 Probability
Abstract
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.
Cite
@article{arxiv.1802.05754,
title = {Extended Mean Field Control Problems: stochastic maximum principle and transport perspective},
author = {Beatrice Acciaio and Julio Backhoff-Veraguas and Rene Carmona},
journal= {arXiv preprint arXiv:1802.05754},
year = {2018}
}
Comments
We changed the title, added an example, and suggest a discretization scheme