# On the Impact of Performative Risk Minimization for Binary Random Variables

arXiv: https://arxiv.org/abs/2502.02331 · HTML: https://mlsanity.com/paper/2502.02331/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [Men Also Like Shopping: Reducing Gender Bias Amplification using Corpus-level Constraints](https://mlsanity.com/paper/1707.09457/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [When Is Partially Observable Reinforcement Learning Not Scary?](https://mlsanity.com/paper/2204.08967/) (2022)
- [Runaway Feedback Loops in Predictive Policing](https://mlsanity.com/paper/1706.09847/) (2017)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Directional Bias Amplification](https://mlsanity.com/paper/2102.12594/) (2021)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Equal Opportunity in Online Classification with Partial Feedback](https://mlsanity.com/paper/1902.02242/) (2019)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Men Also Do Laundry: Multi-Attribute Bias Amplification](https://mlsanity.com/paper/2210.11924/) (2022)
- [Addressing Polarization and Unfairness in Performative Prediction](https://mlsanity.com/paper/2406.16756/) (2024)
- [Diversified Recommendations for Agents with Adaptive Preferences](https://mlsanity.com/paper/2210.07773/) (2022)
- [Dynamic Modeling and Equilibria in Fair Decision Making](https://mlsanity.com/paper/1911.06837/) (2019)
- [Online Control in Population Dynamics](https://mlsanity.com/paper/2406.01799/) (2024)
- [DPA: A one-stop metric to measure bias amplification in classification datasets](https://mlsanity.com/paper/2412.11060/) (2024)

## Built on by (most cited first, 3 of 3)

- [PAC Learnability in the Presence of Performativity](https://mlsanity.com/paper/2510.08335/) (2025)
- [Optimal Regularization for Performative Learning](https://mlsanity.com/paper/2510.12249/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)

## Abstract (arXiv)

Performativity, the phenomenon where outcomes are influenced by predictions, is particularly prevalent in social contexts where individuals strategically respond to a deployed model. In order to preserve the high accuracy of machine learning models under distribution shifts caused by performativity, Perdomo et al. (2020) introduced the concept of performative risk minimization (PRM). While this framework ensures model accuracy, it overlooks the impact of the PRM on the underlying distributions and the predictions of the model. In this paper, we initiate the analysis of the impact of PRM, by studying performativity for a sequential performative risk minimization problem with binary random variables and linear performative shifts. We formulate two natural measures of impact. In the case of full information, where the distribution dynamics are known, we derive explicit formulas for the PRM solution and our impact measures. In the case of partial information, we provide performative-aware statistical estimators, as well as simulations. Our analysis contrasts PRM to alternatives that do not model data shift and indicates that PRM can have amplified side effects compared to such methods.