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.

翻译：表演性预测会影响它们旨在预测的结果本身。我们研究了影响样本（例如，仅现有应用程序用户）和/或整个总体（例如，所有潜在应用程序用户）的表演性预测。这引发了一个问题：在表演性条件下，模型的泛化能力如何？例如，当新应用程序用户和现有用户都对应用程序的预测做出反应时，我们如何能基于现有用户对新用户得出有效的见解？我们通过将表演性预测嵌入统计学习理论来探讨这个问题。我们证明了在样本、总体以及两者同时受到表演性影响下的泛化界。我们证明背后的一个关键直觉是：在最坏情况下，总体否定预测，而样本则欺骗性地实现预测。我们将这种自我否定和自我实现的预测分别表述为Wasserstein空间中的最小-最大和最小-最小风险泛函。我们的分析揭示了改变世界与从中学习之间的基本权衡：模型对数据的影响越大，它能从中学习到的就越少。此外，我们的分析得出了一个关于如何通过在表演性扭曲的样本上重新训练来改进泛化保证的惊人见解。我们通过一个案例研究来说明我们的界，该研究基于德国1975年至2017年的行政劳动力市场记录，探讨了针对德国失业居民的预测知情工作培训分配。