Learning Strategy-Aware Linear Classifiers
This work addresses strategic classification in machine learning, advancing the literature on learning from revealed preferences, though it is incremental by focusing on linear classifiers and regret bounds.
The paper tackles the problem of learning linear classifiers against strategic agents who try to game the system, using Stackelberg regret as a performance measure. It shows that Stackelberg and external regret are strongly incompatible in worst-case scenarios and presents a strategy-aware algorithm with nearly matching upper and lower regret bounds.
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.