# Optimal Regularization for Performative Learning

arXiv: https://arxiv.org/abs/2510.12249 · HTML: https://mlsanity.com/paper/2510.12249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 51 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 30 of 42)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Benign overfitting in ridge regression](https://mlsanity.com/paper/2009.14286/) (2020)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [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)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [Feedback Loops With Language Models Drive In-Context Reward Hacking](https://mlsanity.com/paper/2402.06627/) (2024)
- [Analysis of classifiers' robustness to adversarial perturbations](https://mlsanity.com/paper/1502.02590/) (2015)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Asymptotics of Ridge (less) Regression under General Source Condition](https://mlsanity.com/paper/2006.06386/) (2020)
- [Data Feedback Loops: Model-driven Amplification of Dataset Biases](https://mlsanity.com/paper/2209.03942/) (2022)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Provable Benefits of Overparameterization in Model Compression: From Double Descent to Pruning Neural Networks](https://mlsanity.com/paper/2012.08749/) (2020)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime](https://mlsanity.com/paper/1911.01544/) (2019)
- [Precise High-Dimensional Asymptotics for Quantifying Heterogeneous Transfers](https://mlsanity.com/paper/2010.11750/) (2020)
- [Towards a statistical theory of data selection under weak supervision](https://mlsanity.com/paper/2309.14563/) (2023)
- [Scaling laws for learning with real and surrogate data](https://mlsanity.com/paper/2402.04376/) (2024)
- [Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents](https://mlsanity.com/paper/2209.03811/) (2022)
- [High-dimensional Analysis of Knowledge Distillation: Weak-to-Strong Generalization and Scaling Laws](https://mlsanity.com/paper/2410.18837/) (2024)
- [Optimal Ridge Regularization for Out-of-Distribution Prediction](https://mlsanity.com/paper/2404.01233/) (2024)

## Built on by (most cited first, 1 of 1)

- [Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing](https://mlsanity.com/paper/2605.20105/) (2026)

## Abstract (arXiv)

In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should thus not only optimize the model for the current data but also take into account that the model might steer the distribution in a new direction, without knowing the exact nature of the potential shift. We explore how regularization can help cope with performative effects by studying its impact in high-dimensional ridge regression. We show that, while performative effects worsen the test risk in the population setting, they can be beneficial in the over-parameterized regime where the number of features exceeds the number of samples. We show that the optimal regularization scales with the overall strength of the performative effect, making it possible to set the regularization in anticipation of this effect. We illustrate this finding through empirical evaluations of the optimal regularization parameter on both synthetic and real-world datasets.