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

TL;DR

This paper introduces a novel approach using approximating Rockafellians to enhance the stability of stochastic programs with respect to distributional perturbations, especially for discontinuous integrands and chance-constrained problems.

Contribution

It extends stability analysis to general distributions and discontinuous integrands, providing new theoretical insights and practical methods for chance-constrained stochastic programming.

Findings

Improved stability results under weaker assumptions.

Applicability to general distributions and discontinuous integrands.

Enhanced robustness of chance-constrained programs.

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.