This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence.

A key contribution  of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods.

We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework.

Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs.

The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems.