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Utility-Fairness Trade-Offs and How to Find Them

Sepehr Dehdashtian, Bashir Sadeghi, Vishnu Naresh Boddeti

TL;DR

The paper tackles the core challenge of balancing predictive utility with demographic fairness by introducing two intrinsic trade-offs: Data-Space Trade-Off (DST) and Label-Space Trade-Off (LST). It then presents U-FaTE, a scalable method that numerically quantifies these trade-offs from data via a closed-form, RKHS-based optimization using a universal dependence measure, enabling practical estimation of the trade-offs for various fairness definitions. The framework facilitates evaluating and comparing representations—across zero-shot CLIP and supervised models—by measuring how far they lie from the estimated DST and LST, revealing that many pre-trained models are far from the theoretical limits; in some cases, extra data can push performance beyond the DST. The work provides extensive empirical results on CelebA, FairFace, and FolkTables, demonstrates the stability of DST/LST estimates, and offers a principled tool for understanding and guiding fair representation learning in high-stakes settings. Overall, U-FaTE and the DST/LST concepts advance quantitative understanding of fairness-utility compromises and offer a practical pathway to assess and improve representations with respect to specified fairness criteria.

Abstract

When building classification systems with demographic fairness considerations, there are two objectives to satisfy: 1) maximizing utility for the specific task and 2) ensuring fairness w.r.t. a known demographic attribute. These objectives often compete, so optimizing both can lead to a trade-off between utility and fairness. While existing works acknowledge the trade-offs and study their limits, two questions remain unanswered: 1) What are the optimal trade-offs between utility and fairness? and 2) How can we numerically quantify these trade-offs from data for a desired prediction task and demographic attribute of interest? This paper addresses these questions. We introduce two utility-fairness trade-offs: the Data-Space and Label-Space Trade-off. The trade-offs reveal three regions within the utility-fairness plane, delineating what is fully and partially possible and impossible. We propose U-FaTE, a method to numerically quantify the trade-offs for a given prediction task and group fairness definition from data samples. Based on the trade-offs, we introduce a new scheme for evaluating representations. An extensive evaluation of fair representation learning methods and representations from over 1000 pre-trained models revealed that most current approaches are far from the estimated and achievable fairness-utility trade-offs across multiple datasets and prediction tasks.

Utility-Fairness Trade-Offs and How to Find Them

TL;DR

The paper tackles the core challenge of balancing predictive utility with demographic fairness by introducing two intrinsic trade-offs: Data-Space Trade-Off (DST) and Label-Space Trade-Off (LST). It then presents U-FaTE, a scalable method that numerically quantifies these trade-offs from data via a closed-form, RKHS-based optimization using a universal dependence measure, enabling practical estimation of the trade-offs for various fairness definitions. The framework facilitates evaluating and comparing representations—across zero-shot CLIP and supervised models—by measuring how far they lie from the estimated DST and LST, revealing that many pre-trained models are far from the theoretical limits; in some cases, extra data can push performance beyond the DST. The work provides extensive empirical results on CelebA, FairFace, and FolkTables, demonstrates the stability of DST/LST estimates, and offers a principled tool for understanding and guiding fair representation learning in high-stakes settings. Overall, U-FaTE and the DST/LST concepts advance quantitative understanding of fairness-utility compromises and offer a practical pathway to assess and improve representations with respect to specified fairness criteria.

Abstract

When building classification systems with demographic fairness considerations, there are two objectives to satisfy: 1) maximizing utility for the specific task and 2) ensuring fairness w.r.t. a known demographic attribute. These objectives often compete, so optimizing both can lead to a trade-off between utility and fairness. While existing works acknowledge the trade-offs and study their limits, two questions remain unanswered: 1) What are the optimal trade-offs between utility and fairness? and 2) How can we numerically quantify these trade-offs from data for a desired prediction task and demographic attribute of interest? This paper addresses these questions. We introduce two utility-fairness trade-offs: the Data-Space and Label-Space Trade-off. The trade-offs reveal three regions within the utility-fairness plane, delineating what is fully and partially possible and impossible. We propose U-FaTE, a method to numerically quantify the trade-offs for a given prediction task and group fairness definition from data samples. Based on the trade-offs, we introduce a new scheme for evaluating representations. An extensive evaluation of fair representation learning methods and representations from over 1000 pre-trained models revealed that most current approaches are far from the estimated and achievable fairness-utility trade-offs across multiple datasets and prediction tasks.
Paper Structure (24 sections, 3 theorems, 32 equations, 5 figures, 2 tables)

This paper contains 24 sections, 3 theorems, 32 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. The Utility-Fairness Trade-Offs
  4. Numerically Quantifying the Trade-Offs
  5. Problem Setup
  6. Optimization via Dependence Measures
  7. A Solution to the Optimization Problem
  8. Numerically Estimating the LST
  9. Scheme for Evaluating Representations
  10. Experimental Evaluation
  11. Experimental Setup
  12. Evaluating FRL Methods
  13. Evaluating Zero-Shot CLIP Models
  14. Evaluating Supervised Representations
  15. Concluding Remarks
  16. ...and 9 more sections

Key Result

Theorem 1

A global optimizer of eq:main-kernel-new is where $\bm \Theta^{\text{opt}}_{Enc}=\bm U^T \bm L_{\tilde{X}}^\dagger\in \mathbb R^{r\times n}$ and the columns of $\bm U$ are eigenvectors corresponding to the $r$ largest eigenvalues of the following generalized eigenvalue problem. Here $\bm L_{\tilde{X}}\bm L_{\tilde{X}}^T=\bm K_{\tilde{X}}$, ${\tilde{X}}_c \sim p(\tilde{X}|Y=y)$ and $S_c \sim p(S|

Figures (5)

  • Figure 1: The utility-fairness trade-offs. (a) Classification systems can be evaluated by their utility (e.g., accuracy) w.r.t. a target label $Y$ and their unfairness w.r.t. a demographic label $S$. We introduce two trade-offs, Data Space Trade-Off (DST) and Label Space Trade-Off (LST). (b) We empirically estimate DST and LST on CelebA and evaluate the utility (high cheekbones) and fairness (gender & age) of over 100 zero-shot and 900 supervised models.
  • Figure 2: Overview of U-FaTE: (Left) It comprises two components, a feature extractor and a fair encoder, that are trained end-to-end. Once U-FaTE is trained, the MLP classifier is trained to predict $Y$ from which fairness metrics can be computed. (Right) The fair encoder parameters are optimized through a closed-form solver operating on the features from the feature extractor. See text for more details.
  • Figure 3: Evaluating Fair Representation Learning Methods: Accuracy versus fairness trade-offs on CelebA (a)-(c) and FolkTable (d)-(f). (a) and (d) show the trade-off for Equalized Opportunity as the fairness constraint. (b) and (e) show the trade-off for Equality of Odds as the fairness constraint, and (c) and (f) show the trade-off for Demographic Parity as the fairness constraint. The solid lines represent the mean accuracy at a given fairness value, and the shaded region shows the uncertainty of the trade-off. Both DST and LST estimates from U-FaTE are stable. Among the FRL methods, K-$\mathcal{T}_{\text{Opt}}$ is closest to the DST, while ARL has the most variance.
  • Figure 4: Evalauting Pre-Trained Zero-Shot and Supervised Models: Accuracy-fairness evaluation of more than 100 pre-trained zero-shot models on CelebA (a) and FairFace (b), and over 900 pre-trained image representations on CelebA (c), and FairFace (d).
  • Figure 5: Training process of U-FaTE contains two phases. Phase 1: The closed-form solution for the encoder is calculated using the features generated by the feature extractor while its parameters are frozen. Phase 2: The feature extractor is trained using the loss provided by the calculated encoder parameters from Phase 1.

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof