arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2603.00537cs.LGcs.DB
收藏

累积分布函数上线性回归的投毒攻击数学基础

Mathematical Foundations of Poisoning Attacks on Linear Regression over Cumulative Distribution Functions

Graduate School of Information Science and Technology, The University of Tokyo(东京大学信息科学与技术研究生院);Algorithms Group, IT University of Copenhagen(哥本哈根IT大学算法组)

Atsuki Sato, Martin Aumüller, Yusuke Matsui

AI总结:

本文研究了累积分布函数上线性回归模型的投毒攻击,分析了单点和多点攻击的理论性质,并提出方法计算攻击影响上界。

摘要:

已学习索引是一类索引数据结构,通过使用机器学习模型近似累积分布函数(CDF)来实现快速搜索(Kraska等,SIGMOD'18)。然而,最近的研究表明,已学习索引容易受到投毒攻击的影响,向训练数据中注入少量毒键可以显著降低模型精度并减少索引性能(Kornaropoulos等,SIGMOD'22)。在本文中,我们对针对CDF上的线性回归模型的投毒攻击进行了严格的理论分析,线性回归是最重要的基本回归模型之一,并且是许多已学习索引的核心组成部分。我们的主要贡献如下:(i)我们提出了一个理论证明,表征了最优单点投毒攻击,并表明现有方法得到的攻击是最佳的。(ii)我们证明在多点攻击中,现有贪心方法并不总是最优的,并且严格推导了最优攻击应满足的关键属性。(iii)我们提出了一种计算多点投毒攻击影响上界的方法,并通过实验证明,贪心方法下的损失往往接近这个上界。我们的研究加深了对线性回归模型在CDF上的攻击策略的理论理解,并为已学习索引的攻击和防御的理论评估提供了基础。

英文摘要:

Learned indexes are a class of index data structures that enable fast search by approximating the cumulative distribution function (CDF) using machine learning models (Kraska et al., SIGMOD'18). However, recent studies have shown that learned indexes are vulnerable to poisoning attacks, where injecting a small number of poison keys into the training data can significantly degrade model accuracy and reduce index performance (Kornaropoulos et al., SIGMOD'22). In this work, we provide a rigorous theoretical analysis of poisoning attacks targeting linear regression models over CDFs, one of the most basic regression models and a core component in many learned indexes. Our main contributions are as follows: (i) We present a theoretical proof characterizing the optimal single-point poisoning attack and show that the existing method yields the optimal attack. (ii) We show that in multi-point attacks, the existing greedy approach is not always optimal, and we rigorously derive the key properties that an optimal attack should satisfy. (iii) We propose a method to compute an upper bound of the multi-point poisoning attack's impact and empirically demonstrate that the loss under the greedy approach is often close to this bound. Our study deepens the theoretical understanding of attack strategies against linear regression models on CDFs and provides a foundation for the theoretical evaluation of attacks and defenses on learned indexes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑