Fast & Fair: Efficient Second-Order Robust Optimization for Fairness in Machine Learning

TL;DR

The paper addresses fairness in machine learning by marrying adversarial training with robust optimization, solving a min–max objective where inner input perturbations are constrained to a radius $r$ and the outer objective optimizes model parameters. It introduces a second-order trust region subproblem (TRS) approach to efficiently solve the inner optimization, deriving a practical update that leverages the Hessian with respect to inputs and a bisection routine to enforce the perturbation constraint. Empirical results on synthetic data and real-world datasets (Adult and LSAT) show potential fairness improvements in training with certain radii, while revealing trade-offs in accuracy and dataset-dependent behavior; TRS consistently outperforms PGD in inner-optimization speed, often by large factors, and random perturbations remain the fastest baseline. The work demonstrates meaningful speedups from second-order information in robust fairness training and outlines avenues for extending to deeper architectures, multiclass settings, and stronger fairness guarantees.

Abstract

This project explores adversarial training techniques to develop fairer Deep Neural Networks (DNNs) to mitigate the inherent bias they are known to exhibit. DNNs are susceptible to inheriting bias with respect to sensitive attributes such as race and gender, which can lead to life-altering outcomes (e.g., demographic bias in facial recognition software used to arrest a suspect). We propose a robust optimization problem, which we demonstrate can improve fairness in several datasets, both synthetic and real-world, using an affine linear model. Leveraging second order information, we are able to find a solution to our optimization problem more efficiently than a purely first order method.

Figures (7)

• Figure 1: Robust optimization, visualized in the case of a linear classifier (black line) in two dimensions $\mathbf{w}^\top \mathbf{z} + b = 0$. The black data points $\mathbf{z} \equiv f_{\text{\boldmath$\mathbf{\theta}$}}(\mathbf{x})$ are the network outputs for various data inputs. The white circles indicate output features within a radius of $r$ of the network outputs. The direction of perturbation $\text{\boldmath$\mathbf{\delta}$}_{\mathbf{z}}$ that maximizes the inner optimization problem is normal to the linear classifier defined by $\mathbf{w}$. Any network outputs in the white channel, $r$ away from the linear classifier, change the predicted class. Robust optimization encourages network outputs to live outside of the white channel to avoid ambiguous class predictions.
• Figure 1: Flattening behavior of sigmoidal function, $\sigma$, derivatives.
• Figure 1: Points are colored based on their original location in the blue region ($Y = 1$) or red region ($Y = 0$). Post shift, note the unfair presence of red $B$s in the blue region and blue $A$s in the red region.
• Figure 2: Comparative Analysis of Non-Robust and Robust Classifiers
• Figure 3: Fairness differences (r=0.18). Left bar is nonrobust, middle is random, right is robust.