Title: Linear Strategic Classification with Endogenous Improvements

Original: arXiv:2606.01198v1 Announce Type: new 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.

Rewritten:

Title: Linear Strategic Classification with Endogenous Improvements

Abstract: Strategic classification examines scenarios where individuals adapt to a deployed classifier by altering their observable characteristics, incurring associated costs. Traditional frameworks often view these adaptations as superficial, meaning that while features might shift, the underlying true labels stay constant. In contrast, we investigate an "improvement-aware" framework where strategic actions can lead to authentic modifications in features that directly influence outcomes. In this model, agents select their post-deployment feature vectors strategically, after which labels are produced via a stable conditional outcome rule that maintains the integrity of the feature-outcome relationship. We define this problem specifically for linear classifiers, assuming a single-index qualification model and costs that are linearly decomposable. Our analysis demonstrates that the classifier optimal from a strategic perspective is derived by applying a parallel translation to the Bayes-optimal decision boundary. Furthermore, this strategic-optimal classifier serves as a superior approximation for the improvement-aware objective compared to the standard Bayes classifier. Because learning in an improvement-aware context necessitates access to post-deployment labels—data that is generally inaccessible prior to deployment—we offer PAC-style guarantees within an oracle framework. Additionally, we introduce a feasible plug-in algorithm, derive its generalization bounds, and validate its performance using both synthetic and real-world datasets.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC