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Description
Adversarial training procedures can alleviate the problem of overfitting in multi-class classification. Exploring this approach from a distributional perspective leads to robust optimization using a Wasserstein distance. Recent theoretical results 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; the number of unknowns scales polynomially with the number of data points and even exponentially with the number of classes. 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. For details, see the accompanying preprint: arXiv:2406.08331
