Incentive-aware PAC learning

We study PAC learning in the presence of strategic manipulation, where data points may modify their features in certain predefined ways in order to receive a better outcome. We show that the vanilla ERM principle fails to achieve any nontrivial guarantee in this context. Instead, we propose an incentive-aware version of the ERM principle which has asymptotically optimal sample complexity. We then focus our attention on incentive-compatible classifiers, which provably prevent any kind of strategic manipulation. We give a sample complexity bound that is, curiously, independent of the hypothesis class, for the ERM principle restricted to incentivecompatible classifiers. This suggests that incentive compatibility alone can act as an effective means of regularization. We further show that it is without loss of generality to consider only incentive-compatible classifiers when opportunities for strategic manipulation satisfy a transitivity condition. As a consequence, in such cases, our hypothesis-classindependent sample complexity bound applies even without incentive compatibility. Our results set the foundations of incentive-aware PAC learning.