On the Impact of Performative Risk Minimization for Binary Random Variables

2025-02-04

AI Summary

This paper investigates the modeling implications of Predictive Risk Minimization (PRM) under binary response variables and linear representational shifts. Addressing the critical issue that PRM may amplify distributional deterioration, we propose two interpretable influence measures and derive their closed-form solutions under full-information settings and statistically consistent estimators with theoretical guarantees under partial-information settings. To our knowledge, this is the first work to systematically quantify PRM’s adverse side effects, revealing that—contrary to intuition—PRM can exacerbate negative distributional drift relative to static methods that ignore shift. Through analytical optimization, deployability-aware estimation, and Monte Carlo simulations, we demonstrate that while PRM improves short-term predictive robustness, it may induce more severe long-term distributional degradation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Preferences

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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Performativity, the phenomenon where outcomes are influenced by predictions, is particularly prevalent in social contexts where individuals strategically respond to a deployed model. In order to preserve the high accuracy of machine learning models under distribution shifts caused by performativity, Perdomo et al. (2020) introduced the concept of performative risk minimization (PRM). While this framework ensures model accuracy, it overlooks the impact of the PRM on the underlying distributions and the predictions of the model. In this paper, we initiate the analysis of the impact of PRM, by studying performativity for a sequential performative risk minimization problem with binary random variables and linear performative shifts. We formulate two natural measures of impact. In the case of full information, where the distribution dynamics are known, we derive explicit formulas for the PRM solution and our impact measures. In the case of partial information, we provide performative-aware statistical estimators, as well as simulations. Our analysis contrasts PRM to alternatives that do not model data shift and indicates that PRM can have amplified side effects compared to such methods.

Problem

• Impact of performative risk minimization
• Binary random variables analysis
• Linear performative shifts effects

Innovation

• Performative Risk Minimization framework
• Binary random variables analysis
• Performative-aware statistical estimators