# Optimal Classification under Performative Distribution Shift

arXiv: https://arxiv.org/abs/2411.02023 · HTML: https://mlsanity.com/paper/2411.02023/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Regularization properties of adversarially-trained linear regression](https://mlsanity.com/paper/2310.10807/) (2023)

## Built on by (most cited first, 10 of 10)

- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Bridging Distribution Shift and AI Safety: Conceptual and Methodological Synergies](https://mlsanity.com/paper/2505.22829/) (2025)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [Optimal Regularization for Performative Learning](https://mlsanity.com/paper/2510.12249/) (2025)
- [Strategically Deceptive Model Deployment in Performative Prediction](https://mlsanity.com/paper/2506.09044/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)
- [Non-Linear Strategic Classification Made Practical](https://mlsanity.com/paper/2606.28204/) (2026)
- [Performative Privacy: When Differential Privacy Maximizes Utility](https://mlsanity.com/paper/2608.28198/) (2026)
- [Partially Informed Stochastic Optimization via Zeroth-Order Residual Tracking](https://mlsanity.com/paper/2610.13871/) (2026)

## Abstract (arXiv)

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these performative effects are modelled as push-forward measures. This general framework encompasses existing models and enables novel performative gradient estimation methods, leading to more efficient and scalable learning strategies. For distribution shifts, unlike previous models which require full specification of the data distribution, we only assume knowledge of the shift operator that represents the performative changes. This approach can also be integrated into various change-of-variablebased models, such as VAEs or normalizing flows. Focusing on classification with a linear-in-parameters performative effect, we prove the convexity of the performative risk under a new set of assumptions. Notably, we do not limit the strength of performative effects but rather their direction, requiring only that classification becomes harder when deploying more accurate models. In this case, we also establish a connection with adversarially robust classification by reformulating the minimization of the performative risk as a min-max variational problem. Finally, we illustrate our approach on synthetic and real datasets.