  In this paper we propose a new methodology for decision-making under
uncertainty using recent advancements in the areas of nonlinear stochastic
optimal control theory, applied mathematics, and machine learning. Grounded on
the fundamental relation between certain nonlinear partial differential
equations and forward-backward stochastic differential equations, we develop a
control framework that is scalable and applicable to general classes of
stochastic systems and decision-making problem formulations in robotics and
autonomy. The proposed deep neural network architectures for stochastic control
consist of recurrent and fully connected layers. The performance and
scalability of the aforementioned algorithm are investigated in three
non-linear systems in simulation with and without control constraints. We
conclude with a discussion on future directions and their implications to
robotics.
