Online Strategic Classification with Noise and Partial Feedback

In this paper, we study an online strategic classification problem, where a principal aims to learn an accurate binary linear classifier from interactions with sequentially arriving agents. For each agent, the principal announces a classifier. The agent can strategically exercise costly manipulations on his features to be classified as the favorable positive class. The principal is unaware of the true featurelabel relationship, but observes all reported features and only labels of positively classified agents. We assume that the true feature-label relationship is given by a halfspace model subject to arbitrary feature-dependent but bounded noise (i.e., Massart noise). This problem faces the combined challenges of agents' strategic feature manipulations, partial feedback observations, and label noise. We tackle these challenges by a novel learning algorithm. We show that the proposed algorithm yields classifiers that converge to the clairvoyant optimal classifier and attains a regret rate of O( T) up to poly-logarithmic and constant factors over T cycles.