arXiv:2501.07275cs.LGmath.OC2025-01

针对含类别特征的岭回归模型,提出新型投毒攻击算法。

Generating Poisoning Attacks against Ridge Regression Models with Categorical Features

  • 将类别特征建模为SOS-1集,构建双层优化攻击框架。
  • 在所有数据集上均优于已有基准,显著提升均方误差。
  • 适用于防御研究者测试模型鲁棒性,尤其关注类别特征场景。

机器学习模型虽能从大数据中提取信息并做出精准预测,但易受外部攻击导致性能下降或行为偏离。其中一种攻击方式是在训练阶段注入恶意数据,即投毒攻击。本文提出一种针对包含数值与类别特征的岭回归模型的强效投毒攻击算法,显式建模并攻击类别特征。将类别特征表示为SOS-1集合,将攻击设计问题建模为上层非凸混合整数、下层无约束凸二次的双层优化问题。给出数学公式,基于下层KKT条件实现单层重构,推导下层变量边界以加速求解,并提出新算法专门用于类别特征投毒。数值实验表明,本方法在所有数据集上的均方误差均优于文献中现有基准。

原文摘要 · Abstract (English)

Machine Learning (ML) models have become a very powerful tool to extract information from large datasets and use it to make accurate predictions and automated decisions. However, ML models can be vulnerable to external attacks, causing them to underperform or deviate from their expected tasks. One way to attack ML models is by injecting malicious data to mislead the algorithm during the training phase, which is referred to as a poisoning attack. We can prepare for such situations by designing anticipated attacks, which are later used for creating and testing defence strategies. In this paper, we propose an algorithm to generate strong poisoning attacks for a ridge regression model containing both numerical and categorical features that explicitly models and poisons categorical features. We model categorical features as SOS-1 sets and formulate the problem of designing poisoning attacks as a bilevel optimization problem that is nonconvex mixed-integer in the upper-level and unconstrained convex quadratic in the lower-level. We present the mathematical formulation of the problem, introduce a single-level reformulation based on the Karush-Kuhn-Tucker (KKT) conditions of the lower level, find bounds for the lower-level variables to accelerate solver performance, and propose a new algorithm to poison categorical features. Numerical experiments show that our method improves the mean squared error of all datasets compared to the previous benchmark in the literature.

投毒攻击岭回归类别特征优化

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