In contrast with standard classification tasks, strategic classification involves agents strategically modifying their features in an effort to receive favorable predictions. For instance, given a classifier determining loan approval based on credit scores, applicants may open or close their credit cards to fool the classifier. The learning goal is to find a classifier robust against strategic manipulations. Various settings, based on what and when information is known, have been explored in strategic classification. In this work, we focus on addressing a fundamental question: the learnability gaps between strategic classification and standard learning. We essentially show that any learnable class is also strategically learnable: we first consider a fully informative setting, where the manipulation structure (which is modeled by a manipulation graph $G^\star$) is known and during training time the learner has access to both the pre-manipulation data and post-manipulation data. We provide nearly tight sample complexity and regret bounds, offering significant improvements over prior results. Then, we relax the fully informative setting by introducing two natural types of uncertainty. First, following Ahmadi et al. (2023), we consider the setting in which the learner only has access to the post-manipulation data. We improve the results of Ahmadi et al. (2023) and close the gap between mistake upper bound and lower bound raised by them. Our second relaxation of the fully informative setting introduces uncertainty to the manipulation structure. That is, we assume that the manipulation graph is unknown but belongs to a known class of graphs. We provide nearly tight bounds on the learning complexity in various unknown manipulation graph settings. Notably, our algorithm in this setting is of independent interest and can be applied to other problems such as multi-label learning.

翻译：与标准分类任务不同，策略分类涉及主体策略性地修改其特征以争取有利预测。例如，在基于信用评分确定贷款审批的分类器场景中，申请人可能通过开通或注销信用卡来欺骗分类器。学习目标是找到一种对策略操纵具有鲁棒性的分类器。基于信息内容与获取时间的差异，策略分类领域已探索多种设定。本文聚焦于解决一个根本性问题：策略分类与标准学习之间的可学习性差距。我们本质性证明，任何可学习类均可实现策略学习：首先考虑完全信息设定，其中操纵结构（由操纵图$G^\star$建模）已知，且学习者在训练阶段能同时获取操纵前与操纵后的数据。我们提供了近乎紧致的样本复杂度与遗憾界，较先前结果有显著改进。随后，我们通过引入两种自然不确定性类型来放松完全信息设定。第一，遵循Ahmadi等人(2023)的思路，考虑学习者仅能获取操纵后数据的设定。我们改进了Ahmadi等人(2023)的结果，并弥合了其提出的错误上界与下界之间的差距。第二类完全信息设定的放松引入操纵结构的不确定性，即假设操纵图未知但属于已知图类，并在多种未知操纵图设定下给出学习复杂度的近乎紧致界。值得注意的是，本设定中的算法具有独立研究价值，可应用于多标签学习等其他问题。