  The solution to a stochastic optimal control problem can be determined by
computing the value function from a discretization of the associated
Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be
reformulated in terms of a pair of forward-backward SDEs, which makes
Monte-Carlo techniques applicable. More recently, the problem has also been
viewed from the perspective of forward and reverse time SDEs and their
associated Fokker-Planck equations. This approach is closely related to
techniques used in diffusion-based generative models. Forward and reverse time
formulations express the value function as the ratio of two probability density
functions; one stemming from a forward McKean-Vlasov SDE and another one from a
reverse McKean-Vlasov SDE. In this paper, we extend this approach to a more
general class of stochastic optimal control problems and combine it with
ensemble Kalman filter type and diffusion map approximation techniques in order
to obtain efficient and robust particle-based algorithms.
