  This paper is motivated by addressing open questions in distributionally
robust chance-constrained programs (DRCCP) using the popular Wasserstein
ambiguity sets. Specifically, the computational techniques for those programs
typically place restrictive assumptions on the constraint functions and the
size of the Wasserstein ambiguity sets is often set using costly
cross-validation (CV) procedures or conservative measure concentration bounds.
In contrast, we propose a practical DRCCP algorithm using kernel maximum mean
discrepancy (MMD) ambiguity sets, which we term MMD-DRCCP, to treat general
nonlinear constraints without using ad-hoc reformulation techniques. MMD-DRCCP
can handle general nonlinear and non-convex constraints with a proven
finite-sample constraint satisfaction guarantee of a dimension-independent
$\mathcal{O}(\frac{1}{\sqrt{N}})$ rate, achievable by a practical algorithm. We
further propose an efficient bootstrap scheme for constructing sharp MMD
ambiguity sets in practice without resorting to CV. Our algorithm is validated
numerically on a portfolio optimization problem and a tube-based
distributionally robust model predictive control problem with non-convex
constraints.
