Forward-Backward RRT: Branched Sampled FBSDEs for Stochastic Optimal Control

We propose a numerical method to solve forward-backward stochastic differential equations (FBSDE) arising in stochastic optimal control problems. Instead of sampling forward paths independently, we demonstrate how a rapidly-exploring random tree (RRT) method can be utilized for the forward integration pass, as long as the controlled drift terms are appropriately compensated in the backward integration pass. We show how a value function approximation is produced by solving a series of function approximation problems backwards in time along the edges of the constructed RRT tree. We employ a local entropy-weighted least squares Monte Carlo (LSMC) method to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. We demonstrate the proposed method and evaluate it on two nonlinear stochastic optimal control problems with non-quadratic running costs, showing that it can greatly improve convergence over previous FBSDE numerical solution methods.