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Distributionally robust chance constrained programs using maximum mean discrepancy
Yassine Nemmour · Bernhard Schölkopf · Jia-Jie Zhu

We study distributionally robust chance constrained programs (DRCCP) with maximum mean discrepancy (MMD) ambiguity sets. We provide an exact reformulation of those problems such that the uncertain constraint is satisfied with a probability larger than a desired risk-level for distributions within the MMD ball around the empirical distribution. Additionally, we highlight how the ambiguity set can be connected to known statistical bounds on the MMD to obtain statistical guarantees for the data-driven DRCCP. Lastly, we validate our reformulation on a numerical example and compare it to the robust scenario approach.

Author Information

Yassine Nemmour (MPI for Intelligent Systems, Tübingen)
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

Jia-Jie Zhu (Weierstrass Institute, Berlin)

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