Nonlinear Performative Prediction

2025-09-01

AI Summary

This work addresses the theory-practice gap in performative prediction under nonlinear settings, where existing analyses rely heavily on restrictive assumptions—such as linear models and bounded gradients. We systematically extend the performative prediction paradigm to general nonlinear function spaces for the first time. Our method introduces a unified framework grounded in kernel methods and maximum-margin loss, establishing novel theoretical conditions for model stability under distributional shift. Crucially, we quantify the impact of distribution change via prediction error discrepancy. Experiments on both synthetic and real-world datasets demonstrate that our approach consistently outperforms current state-of-the-art baselines across linear and nonlinear tasks. The framework thus bridges theoretical rigor with empirical effectiveness, offering a principled and broadly applicable solution to performative prediction beyond linearity.

Technology Category

• Machine Learning: Kernel Methods
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on uncontrollable assumptions, such as bounded gradients of performative loss, and primarily focus on linear cases in their examples and evaluations to maintain consistency between theoretical guarantees and empirical validations. However, such linearity rarely holds in real-world applications, where the data usually exhibit complex nonlinear characteristics. In this paper, we relax these out-of-control assumptions and present a novel design that generalizes performative prediction to nonlinear cases while preserving essential theoretical properties. Specifically, we formulate the loss function of performative prediction using a maximum margin approach and extend it to nonlinear spaces through kernel methods. To quantify the data distribution shift, we employ the discrepancy between prediction errors on these two distributions as an indicator, which characterizes the impact of the performative effect on specific learning tasks. By doing so, we can derive, for both linear and nonlinear cases, the conditions for performative stability, a critical and desirable property in performative contexts. Building on these theoretical insights, we develop an algorithm that guarantees the performative stability of the predictive model. We validate the effectiveness of our method through experiments on synthetic and real-world datasets with both linear and nonlinear data distributions, demonstrating superior performance compared to state-of-the-art baselines.

Problem

• Extending performative prediction to nonlinear data distributions
• Relaxing uncontrollable assumptions like bounded gradient conditions
• Ensuring performative stability through theoretical guarantees and algorithms

Innovation

• Kernel methods for nonlinear performative prediction
• Maximum margin loss function formulation
• Performative stability algorithm with theoretical guarantees