Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 57, Issue 6, Pages 3666-3693Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1196479
Keywords
controlled McKean-Vlasov SDEs; Pontryagin principle; mean-field interaction; casual transport plans
Categories
Funding
- National Science Foundation [DMS-1716673]
- Army Research Office [W911NF-17-1-0578]
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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 forms, which extend the known conditions to this general framework. We suggest a variational approach for 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.
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