Before revision:  We further show that any \epsilon-optimal controls of these discrete-time problems converge to the optimal control of the original problems . To establish the time regularity of optimal controls and the convergence of time discretizations, we extend the canonical path regularity results to general coupled McKean-Vlasov forward-backward stochastic differential equations, which are of independent interest .
After revision:  We further show that any \epsilon-optimal controls of these discrete-time problems converge to the optimal control of the original problems .