We study mean feld 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 sufcient 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.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics
- Casual transport plans
- Controlled McKean-Vlasov SDEs
- Mean-feld interaction
- Pontryagin principle