# Performative Learning Theory

arXiv: https://arxiv.org/abs/2602.04402 · HTML: https://mlsanity.com/paper/2602.04402/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 53 of its 115 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 30 of 53)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility](https://mlsanity.com/paper/1710.11214/) (2017)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Difficult Lessons on Social Prediction from Wisconsin Public Schools](https://mlsanity.com/paper/2304.06205/) (2023)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)

## Abstract (arXiv)

Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on the sample, on the population, and on both. A key intuition behind our proofs is that in the worst case, the population negates predictions, while the sample deceptively fulfills them. We cast such self-negating and self-fulfilling predictions as min-max and min-min risk functionals in Wasserstein space, respectively. Our analysis reveals a fundamental trade-off between performatively changing the world and learning from it: the more a model affects data, the less it can learn from it. Moreover, our analysis results in a surprising insight on how to improve generalization guarantees by retraining on performatively distorted samples. We illustrate our bounds in a case study on prediction-informed assignments of unemployed German residents to job trainings, drawing upon administrative labor market records from 1975 to 2017 in Germany.