Fair and Accurate Regression: Strong Formulations and Algorithms

TL;DR

This paper develops mixed-integer optimization methods for fair regression, providing exact formulations and algorithms that balance fairness and accuracy efficiently, especially for large-scale problems.

Contribution

It introduces novel strong formulations and algorithms for fair regression, including exact solutions and a coordinate descent method for large-scale instances.

Findings

Competitive statistical performance with state-of-the-art methods

Significant reduction in training times

Effective handling of large-scale fair regression problems

Abstract

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times.