  Novel numerical estimators are proposed for the forward-backward stochastic
differential equations (FBSDE) appearing in the Feynman-Kac representation of
the value function. In contrast to the current numerical method approaches
based on discretization of the continuous-time FBSDE results, we propose a
converse approach, by first obtaining a discrete-time approximation of the
on-policy value function, and then developing a discrete-time result which
resembles the continuous-time counterpart. This approach yields improved
numerical estimators in the function approximation phase, and demonstrates
enhanced error analysis for those value function estimators. Numerical results
and error analysis are demonstrated on a scalar nonlinear stochastic optimal
control problem, and they show improvements in the performance of the proposed
estimators in comparison with the state-of-the-art methodologies.
