  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.
