  We propose a new method for the numerical solution of the forward-backward
stochastic differential equations (FBSDE) appearing in the Feynman-Kac
representation of the value function in stochastic optimal control problems.
Using Girsanov's change of probability measures, it is demonstrated how a
McKean-Markov branched sampling method can be utilized for the forward
integration pass, as long as the controlled drift term is appropriately
compensated in the backward integration pass. Subsequently, a numerical
approximation of the value function is proposed by solving a series of function
approximation problems backwards in time along the edges of a space-filling
tree consisting of trajectory samples. Moreover, a local entropy-weighted least
squares Monte Carlo (LSMC) method is developed to concentrate function
approximation accuracy in regions most likely to be visited by optimally
controlled trajectories. The proposed methodology is numerically demonstrated
on linear and nonlinear stochastic optimal control problems with non-quadratic
running costs, which reveal significant convergence improvements over previous
FBSDE-based numerical solution methods.
