Approximating Rockafellians Mitigate Distributional Perturbations: Discontinuous Integrands and Chance-Constrained Applications

Abstract: In this paper, we show how approximating Rockafellians serve as a principled and effective alternative for improving the stability of stochastic programs under distributional changes. Unlike previous efforts that focus on special distributions and continuous integrands, our results accommodate general probability distributions and discontinuous integrands. Thus, our results apply to chance-constrained programs, for which we obtain improved qualitative and quantitative stability results under weaker assumptions pertaining to metric subregularity and upper outer-Minkowski content.