Genetic Column Generation for Computing Lower Bounds for Adversarial Classification

TL;DR

This paper introduces a genetic column generation approach to efficiently compute lower bounds for adversarial risk in multi-class classification, addressing high-dimensional challenges by leveraging optimal transport techniques.

Contribution

It adapts genetic column generation methods from optimal transport to improve the computation of adversarial risk bounds in high-dimensional classification problems.

Findings

Successfully reduces computational complexity in high dimensions.

Provides tighter lower bounds for adversarial risk.

Demonstrates effectiveness on multi-class classification tasks.

Abstract

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.