Linear Strategic Classification with Endogenous Improvements
This work addresses the problem of designing classifiers that incentivize genuine improvements in agents' features, which is important for socially responsible machine learning applications.
The paper introduces an improvement-aware variant of strategic classification where agents' responses can genuinely improve outcome-relevant features, not just cosmetically alter them. For linear classifiers, they show the strategic-optimal classifier is a parallel shift of the Bayes-optimal boundary and provide PAC guarantees and a plug-in algorithm with strong empirical performance.
Strategic classification studies settings in which agents respond to a deployed classifier by modifying observable features at a cost. Classical models typically treat such responses as cosmetic: features may change, but true labels remain fixed. We study an improvement-aware variant in which strategic responses can induce genuine changes in outcome-relevant features. Agents choose post-deployment feature vectors strategically, and labels are then generated according to a stable conditional outcome law that preserves the relationship between features and outcomes. We formalize this problem for linear classifiers under a single-index qualification model and linear-decomposable costs. We show that the strategic-optimal classifier is obtained by a parallel shift of the Bayes-optimal decision boundary, and that it provides a better surrogate for the improvement-aware objective than the Bayes classifier. Since improvement-aware learning requires post-deployment labels, which are typically unavailable before deployment, we provide PAC-style guar- antees under an oracle model, propose a practical plug-in algorithm, establish its generalization bound, and evaluate it on synthetic and real-world datasets.