# Causal Strategic Linear Regression

arXiv: https://arxiv.org/abs/2002.10066 · HTML: https://mlsanity.com/paper/2002.10066/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 30 of 65)

- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [A Validity Perspective on Evaluating the Justified Use of Data-driven Decision-making Algorithms](https://mlsanity.com/paper/2206.14983/) (2022)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Strategic Ranking](https://mlsanity.com/paper/2109.08240/) (2021)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [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)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Performative Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [Strategic Apple Tasting](https://mlsanity.com/paper/2306.06250/) (2023)
- [Model Transferability With Responsive Decision Subjects](https://mlsanity.com/paper/2107.05911/) (2021)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [Causal Strategic Learning with Competitive Selection](https://mlsanity.com/paper/2308.16262/) (2023)
- [On the Actionability of Outcome Prediction](https://mlsanity.com/paper/2309.04470/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [A Causal Perspective on Meaningful and Robust Algorithmic Recourse](https://mlsanity.com/paper/2107.07853/) (2021)
- [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)

## Abstract (arXiv)

In many predictive decision-making scenarios, such as credit scoring and academic testing, a decision-maker must construct a model that accounts for agents' propensity to "game" the decision rule by changing their features so as to receive better decisions. Whereas the strategic classification literature has previously assumed that agents' outcomes are not causally affected by their features (and thus that strategic agents' goal is deceiving the decision-maker), we join concurrent work in modeling agents' outcomes as a function of their changeable attributes. As our main contribution, we provide efficient algorithms for learning decision rules that optimize three distinct decision-maker objectives in a realizable linear setting: accurately predicting agents' post-gaming outcomes (prediction risk minimization), incentivizing agents to improve these outcomes (agent outcome maximization), and estimating the coefficients of the true underlying model (parameter estimation). Our algorithms circumvent a hardness result of Miller et al. (2020) by allowing the decision maker to test a sequence of decision rules and observe agents' responses, in effect performing causal interventions through the decision rules.