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Data-Driven Chance Constrained Programs over Wasserstein Balls

Zhi Chen (zhi.chen***at***imperial.ac.uk)
Daniel Kuhn (daniel.kuhn***at***epfl.ch)
Wolfram Wiesemann (ww***at***imperial.ac.uk)

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. Using our reformulation, we show that two popular approximation schemes based on the conditional-value-at-risk and the Bonferroni inequality can perform poorly in practice and that these two schemes are generally incomparable with each other.

Keywords: Distributionally robust optimization, ambiguous chance constraints, Wasserstein distance.

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation:

Download: [PDF]

Entry Submitted: 06/22/2018
Entry Accepted: 06/22/2018
Entry Last Modified: 08/31/2018

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