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Creators/Authors contains: "Kim, Jakwang"

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  1. ; ; (, proceedings.mlr.press)
    Free, publicly-accessible full text available May 22, 2026
  2. ; ; (, European Journal of Applied Mathematics)
    Abstract Adversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in their previous work [21]. In addition, we develop new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we provide an alternative proof of the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting. 
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    Free, publicly-accessible full text available December 3, 2025
  3. ; ; ; (, Journal of machine learning research)
    Accepted Manuscript Full Text Available
  4. ; ; (, Journal of machine learning research)
    Bubeck, Sebastien (Ed.)
    We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimarginal optimal transport problems where the number of marginals is equal to the number of classes in the original classification problem. These new theoretical results reveal a rich geometric structure of adversarial learning problems in multiclass classification and extend recent results restricted to the binary classification setting. A direct computational implication of our results is that by solving either the barycenter problem and its dual, or the MOT problem and its dual, we can recover the optimal robust classification rule and the optimal adversarial strategy for the original adversarial problem. Examples with synthetic and real data illustrate our results. 
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    Accepted Manuscript Full Text Available