  Deep learning algorithms have been widely used to solve linear Kolmogorov
partial differential equations~(PDEs) in high dimensions, where the loss
function is defined as a mathematical expectation. We propose to use the
randomized quasi-Monte Carlo (RQMC) method instead of the Monte Carlo (MC)
method for computing the loss function. In theory, we decompose the error from
empirical risk minimization~(ERM) into the generalization error and the
approximation error. Notably, the approximation error is independent of the
sampling methods. We prove that the convergence order of the mean
generalization error for the RQMC method is $O(n^{-1+\epsilon})$ for
arbitrarily small $\epsilon>0$, while for the MC method it is
$O(n^{-1/2+\epsilon})$ for arbitrarily small $\epsilon>0$. Consequently, we
find that the overall error for the RQMC method is asymptotically smaller than
that for the MC method as $n$ increases. Our numerical experiments show that
the algorithm based on the RQMC method consistently achieves smaller relative
$L^{2}$ error than that based on the MC method.
