The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely adversarial or always equally prefers the positive label. In this paper, we generalize both of these through a unified framework for strategic classification, and introduce the notion of strategic VC-dimension (SVC) to capture the PAC-learnability in our general strategic setup. SVC provably generalizes the recent concept of adversarial VC-dimension (AVC) introduced by Cullina et al. arXiv:1806.01471. We instantiate our framework for the fundamental strategic linear classification problem. We fully characterize: (1) the statistical learnability of linear classifiers by pinning down its SVC; (2) its computational tractability by pinning down the complexity of the empirical risk minimization problem. Interestingly, the SVC of linear classifiers is always upper bounded by its standard VC-dimension. This characterization also strictly generalizes the AVC bound for linear classifiers in arXiv:1806.01471.

翻译：对测试数据进行战略或对抗性操纵以愚弄一个分类器的研究最近引起许多注意,以前的工作大多集中于两个极端情况,即任何测试数据点要么是完全对立的,要么总是同样倾向于正面标签。在本文件中,我们通过统一的战略分类框架,对这两种情况加以概括,并引入了战略VC分门化概念,以便在我们的总体战略结构中捕捉PAC分辨性概念。SVC可以明显地概括了Cullina et al. arXiv:1806.011.我们为基本战略线性分类问题制定的框架。我们充分描述:(1) 线性分类者的统计学习能力,将SVC分解到最低程度的复杂经验风险中;有趣的是,线性分类器的SVC总是受其标准的VC分门化(VC-dion):1806.IV。这种定性还严格地将AVC分解的AVC分解器在AX.X.6.IV中的直线性分类器一般。