  Recent theoretical results on adversarial multi-class classification showed a
similarity to the multi-marginal formulation of Wasserstein-barycenter in
optimal transport. Unfortunately, both problems suffer from the curse of
dimension, making it hard to exploit the nice linear program structure of the
problems for numerical calculations. We investigate how ideas from Genetic
Column Generation for multi-marginal optimal transport can be used to overcome
the curse of dimension in computing the minimal adversarial risk in multi-class
classification.
