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.

翻译：近期关于对抗多类别分类的理论研究显示，其与最优传输中Wasserstein重心问题的多边际形式存在相似性。遗憾的是，这两个问题均受维度灾难的困扰，难以利用问题本身优良的线性规划结构进行数值计算。本文研究如何将多边际最优传输中的遗传列生成思想应用于多类别分类中最小对抗风险的计算，以克服维度灾难问题。