  We explore the application of the quasi-Monte Carlo (QMC) method in deep
backward dynamic programming (DBDP) (Hure et al. 2020) for numerically solving
high-dimensional nonlinear partial differential equations (PDEs). Our study
focuses on examining the generalization error as a component of the total error
in the DBDP framework, discovering that the rate of convergence for the
generalization error is influenced by the choice of sampling methods.
Specifically, for a given batch size $m$, the generalization error under QMC
methods exhibits a convergence rate of $O(m^{-1+\varepsilon})$, where
$\varepsilon$ can be made arbitrarily small. This rate is notably more
favorable than that of the traditional Monte Carlo (MC) methods, which is
$O(m^{-1/2+\varepsilon})$. Our theoretical analysis shows that the
generalization error under QMC methods achieves a higher order of convergence
than their MC counterparts. Numerical experiments demonstrate that QMC indeed
surpasses MC in delivering solutions that are both more precise and stable.
