Linear Strategic Classification with Endogenous Improvements

• URL: http://arxiv.org/abs/2606.01198v1
• Date: Sun, 31 May 2026 12:22:30 GMT
• Title: Linear Strategic Classification with Endogenous Improvements
• Abstract summary: We study an improvement-aware variant in which strategic responses can induce genuine changes in outcome-relevant features.<n>Agents choose post-deployment feature vectors strategically, and labels are then generated according to a stable conditional outcome law.
• Score: 6.798190446932253
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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