Data-Driven Chance Constrained Programs over Wasserstein Balls

TL;DR

This paper introduces an exact reformulation for data-driven chance constrained programs over Wasserstein balls, enabling more efficient optimization by converting them into mixed-integer conic or linear programs.

Contribution

It provides a novel deterministic reformulation for chance constrained programs over Wasserstein balls, including special cases that simplify to mixed-integer linear programs.

Findings

Reformulation as mixed-integer conic programs for general Wasserstein balls.

Special case reformulation as mixed-integer linear programs for 1-norm and infinity-norm balls.

Outperforms existing data-driven optimization methods in numerical experiments.

Abstract

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 favourably to several state-of-the-art data-driven optimization schemes in our numerical experiments.