# Performative Prediction with Neural Networks

arXiv: https://arxiv.org/abs/2304.06879 · HTML: https://mlsanity.com/paper/2304.06879/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 14 Apr 2023.

## Builds on (most cited first, 18 of 18)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Breaking the Curse of Dimensionality with Convex Neural Networks](https://mlsanity.com/paper/1412.8690/) (2014)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (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)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [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)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Breaking Feedback Loops in Recommender Systems with Causal Inference](https://mlsanity.com/paper/2207.01616/) (2022)
- [Approximate Regions of Attraction in Learning with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.00055/) (2021)

## Built on by (most cited first, 30 of 34)

- [On the Stability of Iterative Retraining of Generative Models on their own Data](https://mlsanity.com/paper/2310.00429/) (2023)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Addressing Polarization and Unfairness in Performative Prediction](https://mlsanity.com/paper/2406.16756/) (2024)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [The Risks of Recourse in Binary Classification](https://mlsanity.com/paper/2306.00497/) (2023)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Clipped SGD Algorithms for Performative Prediction: Tight Bounds for Clipping Bias and Remedies](https://mlsanity.com/paper/2404.10995/) (2024)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [Statistical Inference under Performativity](https://mlsanity.com/paper/2505.18493/) (2025)
- [The Stability of Online Algorithms in Performative Prediction](https://mlsanity.com/paper/2602.24207/) (2026)
- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions](https://mlsanity.com/paper/2402.15188/) (2024)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)
- [SPRINT: Stochastic Performative Prediction With Variance Reduction](https://mlsanity.com/paper/2509.17304/) (2025)
- [Learn to Evolve: Self-supervised Neural JKO Operator for Wasserstein Gradient Flow](https://mlsanity.com/paper/2601.05583/) (2026)
- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [When and How Human Curation Backfires: Preference Alignment under Multi-Model Self-Consuming Loop](https://mlsanity.com/paper/2605.29267/) (2026)
- [Partially Performative Prediction](https://mlsanity.com/paper/2606.07890/) (2026)
- [Solving Hidden Monotone Variational Inequalities with Surrogate Losses](https://mlsanity.com/paper/2411.05228/) (2024)
- [Optimal Regularization for Performative Learning](https://mlsanity.com/paper/2510.12249/) (2025)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [Retraining Seeks Stable Signals](https://mlsanity.com/paper/2607.15623/) (2026)
- [Strategically Deceptive Model Deployment in Performative Prediction](https://mlsanity.com/paper/2506.09044/) (2025)
- [Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps](https://mlsanity.com/paper/2509.02619/) (2025)
- [Computing Strategic Responses to Non-Linear Classifiers](https://mlsanity.com/paper/2511.21560/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)

## Abstract (arXiv)

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard convergence results for finding a performatively stable classifier with the method of repeated risk minimization assume that the data distribution is Lipschitz continuous to the model's parameters. Under this assumption, the loss must be strongly convex and smooth in these parameters; otherwise, the method will diverge for some problems. In this work, we instead assume that the data distribution is Lipschitz continuous with respect to the model's predictions, a more natural assumption for performative systems. As a result, we are able to significantly relax the assumptions on the loss function. In particular, we do not need to assume convexity with respect to the model's parameters. As an illustration, we introduce a resampling procedure that models realistic distribution shifts and show that it satisfies our assumptions. We support our theory by showing that one can learn performatively stable classifiers with neural networks making predictions about real data that shift according to our proposed procedure.