Distributionally Robust Chance-Constrained Optimization with Deep Kernel Ambiguity Set

Abstract

A distributionally robust chance-constrained programming (DRCCP) approach based on the deep kernel ambiguity set is proposed in this paper. The kernel ambiguity set possesses notable advantages over other existing ambiguity sets from the literature, and it is constructed by using the kernel mean embedding (KME) and the maximum mean discrepancy (MMD) between distributions. In the proposed method, the worst-case Conditional Value-at-Risk (CVaR) approximation is employed to approximate the distributionally robust joint chance constraint (DRJCC). Additionally, the performance of the presented method can be significantly enhanced by using the multi-layer deep arc-cosine kernel (MLACK), compared to the use of shallow kernels. The presented DRCCP approach is applied to a numeral example and a nonlinear process optimization problem to demonstrate its efficacy.