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<p>Based on the Wasserstein distance, we study the distributionally robust optimization problem whose objective function is the probability of an aversion event. We reformulate the specific dual problem and, in the context of a linear classifier adversarial classification problem, we derive exact tractable forms. In addition, we provide a smoothing approximation approach that applies to arbitrary orders of the Wasserstein ball to make the above form convenient to solve. When taking the order as 1, our model corresponds to a classifier training model that already exists, but which fails to work well when the perturbation ratio is large. Therefore, we integrate theoretical analyses and experiments to illustrate that a higher-order model has strong stability and better classification accuracy.</p>

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Optional-Order Distributionally Robust Optimization and Applications in Adversarial Classification

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Huan-Cheng Lin,
  • Yan-Jun Wang

摘要

Based on the Wasserstein distance, we study the distributionally robust optimization problem whose objective function is the probability of an aversion event. We reformulate the specific dual problem and, in the context of a linear classifier adversarial classification problem, we derive exact tractable forms. In addition, we provide a smoothing approximation approach that applies to arbitrary orders of the Wasserstein ball to make the above form convenient to solve. When taking the order as 1, our model corresponds to a classifier training model that already exists, but which fails to work well when the perturbation ratio is large. Therefore, we integrate theoretical analyses and experiments to illustrate that a higher-order model has strong stability and better classification accuracy.