# Linear Strategic Classification with Endogenous Improvements

arXiv: https://arxiv.org/abs/2606.01198 · HTML: https://mlsanity.com/paper/2606.01198/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 39 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 30 of 30)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [On classification of strategic agents who can both game and improve](https://mlsanity.com/paper/2203.00124/) (2022)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [Fundamental Bounds on Online Strategic Classification](https://mlsanity.com/paper/2302.12355/) (2023)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty](https://mlsanity.com/paper/2502.06749/) (2025)
- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)
- [PAC Learning with Improvements](https://mlsanity.com/paper/2503.03184/) (2025)
- [HELOC Applicant Risk Performance Evaluation by Topological Hierarchical Decomposition](https://mlsanity.com/paper/1811.10658/) (2018)
- [Nonparametric logistic regression with deep learning](https://mlsanity.com/paper/2401.12482/) (2024)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [Conservative classifiers do consistently well with improving agents: characterizing statistical and online learning](https://mlsanity.com/paper/2506.05252/) (2025)
- [Desirable Effort Fairness and Optimality Trade-offs in Strategic Learning](https://mlsanity.com/paper/2510.19098/) (2025)
- [Multi-Level Strategic Classification: Incentivizing Improvement through Promotion and Relegation Dynamics](https://mlsanity.com/paper/2602.11439/) (2026)

## Abstract (arXiv)

Classical models of strategic classification treat agents' responses to a deployed classifier as cosmetic: features change, but true labels do not. We study an improvement-aware variant in which strategic responses can change outcomes: agents choose post-deployment features strategically at a cost, and labels are then drawn from a fixed conditional outcome law. We formalize this problem for linear classifiers under a single-index qualification model and linear-decomposable costs. Under these assumptions, agents' best responses reduce to a closed-form shift of the decision boundary, and the resulting improvement-aware classification problem is learnable with linear sample complexity. As post-deployment labels are unavailable a priori, we begin by establishing a generalization bound with oracle access to the outcome law. One of our main contributions is a practical plug-in algorithm that replaces the oracle with an estimate, together with a bound on its improvement-aware error. We also show that the optimal classifier for standard strategic classification is a better proxy for the improvement-aware objective than the non-strategic Bayes-optimal classifier. Experiments on semi-synthetic and synthetic data support these findings and the plausibility of our assumptions.