  In this paper, we study a discrete-time stochastic optimal control problem
under distribution uncertainty with convex control domain. By weak convergence
method and Sion's minimax theorem, we obtain the variational inequality for
cost functional under a reference probability $P^{\ast}$. Moreover, under the
square integrability condition for noise and control, we establish the
discrete-time stochastic maximum principle under $P^{\ast}$. Finally, we
introduce a backward algorithm to calculate the reference probability
$P^{\ast}$ and the optimal control $u^{\ast}$.
