Unified Inference Framework for Single and Multi-Player Performative Prediction: Method and Asymptotic Optimality

2026-02-03

AI Summary

This work addresses the vulnerability of existing predictive models to feedback loops induced by distribution shifts in both single-agent and multi-agent environments, as well as the absence of a unified statistical inference framework. The paper proposes the first unified inferential theory for performative prediction that encompasses both settings, treating the single-agent case as a special instance of the multi-agent scenario. By integrating repeated risk minimization (RRM), recalibrated prediction-driven inference (RePPI), and importance sampling, the authors construct an estimator that achieves asymptotic normality and semiparametric efficiency. This estimator remains robust under mild distributional misspecification, attains the semiparametric efficiency bound, and offers both asymptotic optimality and computational tractability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

Problem

• performative prediction
• single-agent
• multi-agent
• statistical inference
• feedback loops

Innovation

• performative prediction
• unified inference framework
• Repeated Risk Minimization
• RePPI
• semiparametric efficiency