  We address the question of repeatedly learning linear classifiers against
agents who are strategically trying to game the deployed classifiers, and we
use the Stackelberg regret to measure the performance of our algorithms. First,
we show that Stackelberg and external regret for the problem of strategic
classification are strongly incompatible: i.e., there exist worst-case
scenarios, where any sequence of actions providing sublinear external regret
might result in linear Stackelberg regret and vice versa. Second, we present a
strategy-aware algorithm for minimizing the Stackelberg regret for which we
prove nearly matching upper and lower regret bounds. Finally, we provide
simulations to complement our theoretical analysis. Our results advance the
growing literature of learning from revealed preferences, which has so far
focused on "smoother" assumptions from the perspective of the learner and the
agents respectively.
