# Stateful Strategic Regression

arXiv: https://arxiv.org/abs/2106.03827 · HTML: https://mlsanity.com/paper/2106.03827/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [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)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [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)
- [Discrimination in Online Ad Delivery](https://mlsanity.com/paper/1301.6822/) (2013)
- [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)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [A Short-term Intervention for Long-term Fairness in the Labor Market](https://mlsanity.com/paper/1712.00064/) (2017)
- [What does it mean to solve the problem of discrimination in hiring? Social, technical and legal perspectives from the UK on automated hiring systems](https://mlsanity.com/paper/1910.06144/) (2019)
- [From Fair Decision Making to Social Equality](https://mlsanity.com/paper/1812.02952/) (2018)
- [Downstream Effects of Affirmative Action](https://mlsanity.com/paper/1808.09004/) (2018)
- [Simple versus Optimal Contracts](https://mlsanity.com/paper/1808.03713/) (2018)
- [Efficient Convex Optimization with Membership Oracles](https://mlsanity.com/paper/1706.07357/) (2017)
- [Strategyproof Linear Regression in High Dimensions](https://mlsanity.com/paper/1805.10693/) (2018)
- [Watch and Learn: Optimizing from Revealed Preferences Feedback](https://mlsanity.com/paper/1504.01033/) (2015)
- [Truthful Linear Regression](https://mlsanity.com/paper/1506.03489/) (2015)
- [Multidimensional Dynamic Pricing for Welfare Maximization](https://mlsanity.com/paper/1607.05397/) (2016)

## Built on by (most cited first, 30 of 32)

- [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)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods](https://mlsanity.com/paper/2207.02829/) (2022)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [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)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty](https://mlsanity.com/paper/2502.06749/) (2025)
- [Setting Fair Incentives to Maximize Improvement](https://mlsanity.com/paper/2203.00134/) (2022)
- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)
- [Optimizing the Performative Risk under Weak Convexity Assumptions](https://mlsanity.com/paper/2209.00771/) (2022)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Prediction without Preclusion: Recourse Verification with Reachable Sets](https://mlsanity.com/paper/2308.12820/) (2023)
- [The Backfiring Effect of Weak AI Safety Regulation](https://mlsanity.com/paper/2503.20848/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [Explanation Design in Strategic Learning: Sufficient Explanations that Induce Non-harmful Responses](https://mlsanity.com/paper/2502.04058/) (2025)
- [The Disparate Effects of Partial Information in Bayesian Strategic Learning](https://mlsanity.com/paper/2506.00627/) (2025)
- [Multi-Level Strategic Classification: Incentivizing Improvement through Promotion and Relegation Dynamics](https://mlsanity.com/paper/2602.11439/) (2026)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [Stochastic Principal-Agent Problems: Efficient Computation and Learning](https://mlsanity.com/paper/2306.03832/) (2023)
- [Strategic Evaluation: Subjects, Evaluators, and Society](https://mlsanity.com/paper/2310.03655/) (2023)
- [Partial Fairness Awareness: Belief-Guided Strategic Mechanism for Strategic Agents](https://mlsanity.com/paper/2606.00826/) (2026)

## Abstract (arXiv)

Automated decision-making tools increasingly assess individuals to determine if they qualify for high-stakes opportunities. A recent line of research investigates how strategic agents may respond to such scoring tools to receive favorable assessments. While prior work has focused on the short-term strategic interactions between a decision-making institution (modeled as a principal) and individual decision-subjects (modeled as agents), we investigate interactions spanning multiple time-steps. In particular, we consider settings in which the agent's effort investment today can accumulate over time in the form of an internal state - impacting both his future rewards and that of the principal. We characterize the Stackelberg equilibrium of the resulting game and provide novel algorithms for computing it. Our analysis reveals several intriguing insights about the role of multiple interactions in shaping the game's outcome: First, we establish that in our stateful setting, the class of all linear assessment policies remains as powerful as the larger class of all monotonic assessment policies. While recovering the principal's optimal policy requires solving a non-convex optimization problem, we provide polynomial-time algorithms for recovering both the principal and agent's optimal policies under common assumptions about the process by which effort investments convert to observable features. Most importantly, we show that with multiple rounds of interaction at her disposal, the principal is more effective at incentivizing the agent to accumulate effort in her desired direction. Our work addresses several critical gaps in the growing literature on the societal impacts of automated decision-making - by focusing on longer time horizons and accounting for the compounding nature of decisions individuals receive over time.