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This research formalizes the fundamental trade-off in statistical learning where models that actively influence data distributions suffer reduced generalization capabilities. By framing self-fulfilling and self-negating predictions as min-max and min-min risk functionals, the authors provide theoretical bounds showing that retraining on distorted samples can paradoxically improve robustness. The work offers a rigorous framework for understanding how performative effects limit a model's ability to learn from the very data it shapes.
Performative Learning Theory
arXiv:2602.04402v3 Announce Type: replace-cross Abstract: 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.
Abstract: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.
ICML 2026. v2: corrected typo in author list; v3: added explanation of condition 3.2, modified condition 3.3 and fixed lemma 3.4, added examples and explanations in sections 2, 5, and 6
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Computers and Society (cs.CY); Machine Learning (cs.LG); Statistics Theory (math.ST)
arXiv:2602.04402 [stat.ML]
(or arXiv:2602.04402v3 [stat.ML] for this version)
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