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This paper studies distributionally robust chance constrained programs(DRCCPs), where the uncertain constraints must be satisfied with at least aprobability of a prespecified threshold for all probability distributions fromthe Wasserstein ambiguity set. As DRCCPs are often nonconvex and challenging tosolve optimally, researchers have been developing various convex innerapproximations. Recently, ALSO-X has been proven to outperform the conditionalvalue-at-risk (CVaR) approximation of a regular chance constrained program whenthe deterministic set is convex. In this work, we relax this assumption byintroducing a new ALSO-X\# method for solving DRCCPs. Namely, in the bilevelreformulations of ALSO-X and CVaR approximation, we observe that thelower-level ALSO-X is a special case of the lower-level CVaR approximation andthe upper-level CVaR approximation is more restricted than the one in ALSO-X.This observation motivates us to propose the ALSO-X\#, which still resembles abilevel formulation -- in the lower-level problem, we adopt the more generalCVaR approximation, and for the upper-level one, we choose the less restrictedALSO-X. We show that ALSO-X\# can always be better than the CVaR approximationand can outperform ALSO-X under regular chance constrained programs and type$\infty-$Wasserstein ambiguity set. We also provide new sufficient conditionsunder which ALSO-X\# outputs an optimal solution to a DRCCP. We apply theproposed ALSO-X\# to a wireless communication problem and numericallydemonstrate that the solution quality can be even better than the exact method.

ALSO-X#: Better Convex Approximations for Distributionally Robust Chance Constrained Programs