Separation-Utility Pareto Frontier: An Information-Theoretic Characterization

TL;DR

This paper characterizes the trade-off between utility and separation in predictive models using information theory, providing a new regularizer and empirical validation across multiple datasets.

Contribution

It offers a theoretical characterization of the utility-separation Pareto frontier, introduces a CMI-based regularizer for deep models, and empirically demonstrates its effectiveness.

Findings

The Pareto frontier between utility and separation is concave.

The CMI regularizer effectively reduces separation violations.

The method maintains or improves utility while enforcing separation constraints.

Abstract

We study the Pareto frontier (optimal trade-off) between utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome. Through an information-theoretic lens, we prove a characterization of the utility-separation Pareto frontier, establish its concavity, and thereby prove the increasing marginal cost of separation in terms of utility. In addition, we characterize the conditions under which this trade-off becomes strict, providing a guide for trade-off selection in practice. Based on the theoretical characterization, we develop an empirical regularizer based on conditional mutual information (CMI) between predictions and sensitive attributes given the true outcome. The CMI regularizer is compatible with any deep model trained via gradient-based optimization and serves as a scalar monitor of residual separation violations, offering tractable guarantees during training. Finally, numerical experiments support our theoretical findings: across COMPAS, UCI Adult, UCI Bank, and CelebA, the proposed method substantially reduces separation violations while matching or exceeding the utility of established baseline methods. This study thus offers a provable, stable, and flexible approach to enforcing separation in deep learning.