Regularity of the value function and quantitative propagation of chaos for mean field control problems

Understand

We investigate a mean field optimal control problem obtained in the limit of the optimal control of large particle systems with forcing and terminal data which are not assumed to be convex.

• We prove that the value function, which is known to be Lipschitz continuous but not of class C 1 , in general, without convexity, is actually smooth in an open and dense subset of the space of times and probability measures.
• As a consequence, we prove a new quantitative propagation of chaos-type result for the optimal solutions of the particle system starting from this open and dense set.