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We investigate a mean field optimal control problem obtained in the limit ofthe optimal control of large particle systems with forcing and terminal datawhich are not assumed to be convex. We prove that the value function, which isknown to be Lipschitz continuous but not of class C 1 , in general, withoutconvexity, is actually smooth in an open and dense subset of the space of timesand probability measures. As a consequence, we prove a new quantitativepropagation of chaos-type result for the optimal solutions of the particlesystem starting from this open and dense set.

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