Performative Learning Theory

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 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 such questions by embedding performative predictions into statistical learning theory. Our goal is to initiate the study of learnability under performativity. We prove generalization bounds under performative effects on the sample, on the population, and on both. A key intuition behind our results is that in the worst case, the population negates predictions, while the sample deceptively fulfills them. We cast such self-negating and selffulfilling predictions as min-max and min-min risk functionals in Wasserstein space, respectively. Our analysis reveals both a fundamental trade-off between performatively changing the world and learning from it, as well as a surprising insight on how to improve generalization guarantees by retraining on performatively distorted samples. We illustrate our bounds using real data on predictioninformed assignments to job trainings.