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.

对比标准分类任务，战略分类涉及代理人在修改其特征以获得有利预测的过程中的策略性行为，重点关注战略分类与标准学习之间的可学习差距，并通过提供几乎紧密的样本复杂性和后悔界限来解释这一问题，同时引入两种自然的不确定性情况，以实现一定程度的放松的完全信息设置。