# Causal Strategic Classification: A Tale of Two Shifts

arXiv: https://arxiv.org/abs/2302.06280 · HTML: https://mlsanity.com/paper/2302.06280/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 48 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 26 of 26)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [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)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [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)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [On classification of strategic agents who can both game and improve](https://mlsanity.com/paper/2203.00124/) (2022)
- [Learning Losses for Strategic Classification](https://mlsanity.com/paper/2203.13421/) (2022)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Linear Classifiers that Encourage Constructive Adaptation](https://mlsanity.com/paper/2011.00355/) (2020)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [Unfairness Despite Awareness: Group-Fair Classification with Strategic Agents](https://mlsanity.com/paper/2112.02746/) (2021)
- [Strategic Representation](https://mlsanity.com/paper/2206.08542/) (2022)

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

- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [Strategic Apple Tasting](https://mlsanity.com/paper/2306.06250/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [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)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)
- [Performative Prediction on Games and Mechanism Design](https://mlsanity.com/paper/2408.05146/) (2024)
- [Strategic Classification With Externalities](https://mlsanity.com/paper/2410.08032/) (2024)
- [Learning the Distribution Map in Reverse Causal Performative Prediction](https://mlsanity.com/paper/2405.15172/) (2024)
- [How Strategic Agents Respond: Comparing Analytical Models with LLM-Generated Responses in Strategic Classification](https://mlsanity.com/paper/2501.16355/) (2025)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Adversaries With Incentives: A Strategic Alternative to Adversarial Robustness](https://mlsanity.com/paper/2406.11458/) (2024)
- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap](https://mlsanity.com/paper/2502.11981/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [The Disparate Effects of Partial Information in Bayesian Strategic Learning](https://mlsanity.com/paper/2506.00627/) (2025)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [The Role of Causal Features in Strategic Classification for Robustness and Alignment](https://mlsanity.com/paper/2605.27163/) (2026)
- [Learning Under Moral Hazard with Instrumental Regression and Generalized Method of Moments](https://mlsanity.com/paper/2405.20642/) (2024)
- [Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspective](https://mlsanity.com/paper/2505.23954/) (2025)
- [Strategic PAC Learnability via Geometric Definability](https://mlsanity.com/paper/2605.13426/) (2026)
- [Prediction-Intervention Games and Invariant Sets](https://mlsanity.com/paper/2605.16828/) (2026)
- [Partial Fairness Awareness: Belief-Guided Strategic Mechanism for Strategic Agents](https://mlsanity.com/paper/2606.00826/) (2026)
- [Linear Strategic Classification with Endogenous Improvements](https://mlsanity.com/paper/2606.01198/) (2026)
- [Off-Policy Evaluation with Strategic Agents via Local Disclosure](https://mlsanity.com/paper/2606.07308/) (2026)
- [Ambiguous Strategic Classification](https://mlsanity.com/paper/2606.10137/) (2026)
- [Robust Strategic Classification under Decision-Dependent Cost Uncertainty](https://mlsanity.com/paper/2606.30136/) (2026)

## Abstract (arXiv)

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.