The Stability of Online Algorithms in Performative Prediction

2026-02-27

AI Summary

This work addresses the instability of traditional predictive models in performative prediction settings, where deployed algorithms alter data distributions and induce feedback loops. The authors propose an unconditional reduction framework that avoids strong assumptions about how models influence data generation, leveraging randomization and martingale theory to circumvent computational barriers in existing stability analyses. By establishing a theoretical bridge between performative prediction and online learning, they prove that any no-regret algorithm converges to a mixed performative stable equilibrium—where the induced data distribution renders the model’s predictions ex post optimal. This result reveals that common algorithms such as gradient descent inherently possess stabilizing mechanisms that mitigate runaway feedback effects.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in their work on performative prediction. Our main result is an unconditional reduction showing that any no-regret algorithm deployed in performative settings converges to a (mixed) performatively stable equilibrium: a solution in which models actively shape data distributions in ways that their own predictions look optimal in hindsight. Prior to our work, all positive results in this area made strong restrictions on how models influenced distributions. By using a martingale argument and allowing randomization, we avoid any such assumption and sidestep recent hardness results for finding stable models. Lastly, on a more conceptual note, our connection sheds light on why common algorithms, like gradient descent, are naturally stabilizing and prevent runaway feedback loops. We hope our work enables future technical transfer of ideas between online optimization and performativity.

Problem

• performative prediction
• online algorithms
• stability
• feedback loop
• data distribution shift

Innovation

• performative prediction
• no-regret algorithms
• martingale argument
• performatively stable equilibrium
• online learning