On the Computational Complexity of Performative Prediction

2026-01-28

AI Summary

This study addresses the computational complexity of finding ε-execution-stable points in performative prediction under distributional shifts induced by model deployment, particularly in the regime of strong performativity (ρ > 1). By integrating tools from variational inequalities, game theory, and computational complexity theory, the work establishes for the first time that the problem is PPAD-complete when ρ = 1 + O(ε), and extends this hardness result to general convex domains. Furthermore, it demonstrates that computing local optima in strategic classification is PLS-hard. These findings rigorously characterize the intrinsic computational intractability of performative prediction beyond the weak performativity regime and establish its polynomial equivalence to Nash equilibrium computation.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho<1$), the complexity in the regime $\rho>1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete -- and thus polynomial-time equivalent to Nash equilibria in general-sum games -- even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.

Problem

• Performative Prediction
• Computational Complexity
• PPAD-completeness
• Strategic Classification
• Variational Inequalities

Innovation

• performative prediction
• PPAD-completeness
• computational complexity
• strategic classification
• variational inequalities