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Data-Driven Chance Constrained Programs over Wasserstein Balls

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arxiv 1809.00210 v3 pith:RWWMJBQN submitted 2018-09-01 math.OC

Zhi Chen , Daniel Kuhn , Wolfram Wiesemann This is my paper · ORCID
classification math.OC
keywords chanceconstraineddata-drivenprogramreformulationwassersteinballsconstraints
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty-$Wasserstein Distance

    math.OC 2019-08 conditional novelty 6.0 of 10

    Under sign conditions on the technology matrix, the worst-case expected recourse cost in two-stage distributionally robust programs with infinity-Wasserstein ambiguity is exactly a finite linear or conic program with ...

  2. Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

    stat.ML 2019-08 accept novelty 3.0 of 10

    Wasserstein distributionally robust optimization yields data-driven decisions that are computable as convex programs and have finite-sample out-of-sample guarantees, and this tutorial unifies the theory with machine l...

  3. Distributionally Robust Optimization: A Review

    math.OC 2019-08 unverdicted

    A broad review of distributionally robust optimization that organizes the literature by ambiguity-set type and connects DRO to robust optimization, risk aversion, chance constraints, and regularization.

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