Linear Strategic Classification with Endogenous Improvements

2026-05-31

AI Summary

This work addresses a key limitation in conventional strategic classification models, which assume individuals manipulate only superficial features without altering their true labels, thereby ignoring the possibility that strategic behavior may genuinely enhance underlying capabilities. To bridge this gap, we propose an improvement-aware linear strategic classification framework wherein agents’ strategic adjustments can induce real changes in their true labels. Under this setting, we construct a strategy-aware optimal classifier by parallel-shifting the Bayes-optimal decision boundary and provide, for the first time, PAC-style theoretical guarantees alongside a practical plug-in algorithm. Leveraging a single-index merit model, a linearly separable cost function, and a stability condition on outcome laws, our approach—combined with plug-in estimation and generalization bound analysis—demonstrates significant performance gains over standard Bayes classifiers under the improvement-aware objective, as validated on both synthetic and real-world datasets.

Abstract

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.

Problem

• strategic classification
• endogenous improvements
• improvement-aware learning
• linear classifiers
• feature manipulation

Innovation

• strategic classification
• improvement-aware learning
• linear classifiers
• PAC guarantees
• endogenous feature improvement