Data-Driven Chance Constrained Programs over Wasserstein Balls

We provide an exact deterministic reformulation for data-driven, chanceconstrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ???-norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments.

Automated summary

This research provides an exact deterministic reformulation for data-driven, chance-constrained programs over Wasserstein balls. The reformulation converts the problem into a mixed-integer conic program or a mixed-integer linear program, depending on the specific case. Numerical experiments show that this reformulation outperforms several state-of-the-art data-driven optimization schemes.