Technical Note—Data-Driven Chance Constrained Programs over Wasserstein Balls

We provide an exact deterministic reformulation for data-driven, chance-constrained 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 $\infty$-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.

Funding: The authors gratefully acknowledge financial support from the Hong Kong Research Grants Council [Early Career Scheme CityU 21502820], the Swiss National Science Foundation [Grant BSCGI0_157733] as well as the Engineering and Physical Sciences Research Council [Grant EP/N020030/1].