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Addressing Polarization and Unfairness in Performative Prediction

Kun Jin, Tian Xie, Yang Liu, Xueru Zhang

TL;DR

Novel fairness mechanisms are introduced that provably ensure both stability and fairness in performative prediction, validated by theoretical analysis and empirical results.

Abstract

In many real-world applications of machine learning such as recommendations, hiring, and lending, deployed models influence the data they are trained on, leading to feedback loops between predictions and data distribution. The performative prediction (PP) framework captures this phenomenon by modeling the data distribution as a function of the deployed model. While prior work has focused on finding performative stable (PS) solutions for robustness, their societal impacts, particularly regarding fairness, remain underexplored. We show that PS solutions can lead to severe polarization and prediction performance disparities, and that conventional fairness interventions in previous works often fail under model-dependent distribution shifts due to failing the PS criteria. To address these challenges in PP, we introduce novel fairness mechanisms that provably ensure both stability and fairness, validated by theoretical analysis and empirical results.

Addressing Polarization and Unfairness in Performative Prediction

TL;DR

Novel fairness mechanisms are introduced that provably ensure both stability and fairness in performative prediction, validated by theoretical analysis and empirical results.

Abstract

In many real-world applications of machine learning such as recommendations, hiring, and lending, deployed models influence the data they are trained on, leading to feedback loops between predictions and data distribution. The performative prediction (PP) framework captures this phenomenon by modeling the data distribution as a function of the deployed model. While prior work has focused on finding performative stable (PS) solutions for robustness, their societal impacts, particularly regarding fairness, remain underexplored. We show that PS solutions can lead to severe polarization and prediction performance disparities, and that conventional fairness interventions in previous works often fail under model-dependent distribution shifts due to failing the PS criteria. To address these challenges in PP, we introduce novel fairness mechanisms that provably ensure both stability and fairness, validated by theoretical analysis and empirical results.

Paper Structure

This paper contains 49 sections, 19 theorems, 75 equations, 17 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Iterative algorithms to find PS solutions.
  4. Technical conditions for iterative algorithms to converge to PS solutions.
  5. Unfairness and polarization in SDPP
  6. Problem formulation.
  7. Unfairness & polarization effects in SDPP.
  8. Finding Fair-PS solutions
  9. Fair-PS solutions
  10. Existing designs fail to converge to Fair-PS solutions
  11. Novel designs for fairness mechanism
  12. Proposed fair regularization (with and without demographics).
  13. Proposed fair sample re-weighting.
  14. Comparison & discussion.
  15. Theoretical analysis
  16. ...and 34 more sections

Key Result

Lemma 2.4

SDPP problem is guaranteed to have a unique PS solution if all of the following hold: (i) $\ell (\boldsymbol{\theta};Z)$ is $\gamma$-strongly convex; (ii) $\ell (\boldsymbol{\theta};Z)$ is $\beta$-joint smooth; (iii) $\text{T}$ is $\epsilon$-joint sensitive and $\epsilon(1+2\beta/\gamma) < 1$.

Figures (17)

  • Figure 1: Illustrating examples of polarization effects and unfairness of $\boldsymbol{\theta}^{\text{PS}}$ in Prop. \ref{['prop1']} (left) and \ref{['prop2']} (right): dynamics of the group fraction (left) and group-wise accuracy (right) under RRM: the system converges to $(\boldsymbol{\theta}^{\text{PS}}; \mathcal{D}^{\text{PS}})$ that is unfair (details are in App. \ref{['example:ps']}).
  • Figure 2: Results on Gaussian data: Fair-RERM-RW (left), Fair-RERM-GLP (middle), Fair-RERM-SLP (right).
  • Figure 3: Results on Credit data: Fair-RERM-RW (left), Fair-RERM-GLP (middle), Fair-RERM-SLP (right).
  • Figure 4: A Venn diagram of the PP cases.
  • Figure 5: POMDP
  • ...and 12 more figures

Theorems & Definitions (44)

  • Definition 2.1: Strong convexity of loss function
  • Definition 2.2: Joint smoothness of loss function
  • Definition 2.3: Joint sensitivity of transition map
  • Lemma 2.4: Existence of a unique PS solution brown2020performativeperdomo_performative_2021
  • Lemma 2.5: Convergence of iterative algorithms
  • Proposition 3.1: Polarization effects of $\boldsymbol{\theta}^{\text{PS}}$
  • Proposition 3.2: Exacerbated group-wise loss disparity
  • Definition 4.1: Fair-PS solution
  • Example 4.2: Group loss variance as penalty term
  • Example 4.3: Repeated DRO with $\chi^2$-distance metric
  • ...and 34 more