Convergence and Bound Computation for Chance Constrained Distributionally Robust Models using Sample Approximation

TL;DR

This paper develops methods for approximating and bounding solutions to distributionally robust chance constrained models using sample data, ensuring convergence and providing statistical bounds for the optimal value.

Contribution

It introduces a sample approximation approach for distributionally robust chance constraints with general ambiguity sets, proving convergence and establishing statistical bounds.

Findings

Sample approximation converges under certain conditions.

Upper and lower bounds on the optimal value can be statistically estimated.

Applicability to specific ambiguity sets is demonstrated.

Abstract

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower bounds on the optimal value of the model can be estimated statistically. Specific ambiguity sets are discussed as examples.