[Paper Review] Wasserstein Robust Support Vector Machines with Fairness Constraints.

Yijie Wang, Viet Anh Nguyen+1 more|arXiv (Cornell University)|Mar 11, 2021

Adversarial Robustness in Machine Learning9 references4 citations

TL;DR

This paper proposes a Wasserstein robust support vector machine with fairness constraints to improve equality of opportunity in binary classification. By using an ∞-Wasserstein ambiguity set and reformulating worst-case unfairness, the method becomes a mixed-integer program solvable via standard solvers, achieving improved fairness with minimal accuracy loss.

ABSTRACT

We propose a distributionally robust support vector machine with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive an exact reformulation for worst-case unfairness measure. We establish that the model is equivalent to a mixed-binary optimization problem, which can be solved by standard off-the-shelf solvers. We further prove that the expectation of the hinge loss objective function constitutes an upper bound on the misclassification probability. Finally, we numerically demonstrate that our proposed approach improves fairness with negligible loss of predictive accuracy.

Motivation & Objective

• To address fairness in binary classification under distributional uncertainty.
• To ensure classifiers satisfy the equality of opportunity fairness criterion.
• To model distributional ambiguity using an ∞-Wasserstein ball centered at the empirical distribution.
• To derive an exact reformulation of the worst-case unfairness measure for robust optimization.
• To balance fairness improvements with minimal degradation in predictive accuracy.

Proposed method

• Uses a type-∞ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty.
• Derives an exact reformulation of the worst-case unfairness measure under this ambiguity set.
• Reformulates the robust fairness-constrained SVM as a mixed-binary optimization problem.
• Employs standard off-the-shelf solvers to solve the resulting mixed-integer program.
• Uses the expectation of the hinge loss as an upper bound on the misclassification probability.
• Integrates fairness constraints directly into the robust optimization framework via the equality of opportunity criterion.

Experimental results

Research questions

• RQ1 How can distributional robustness be combined with fairness constraints in a support vector machine framework?
• RQ2 What is the exact reformulation of the worst-case unfairness measure under an ∞-Wasserstein ambiguity set?
• RQ3 Can the resulting robust fairness-constrained SVM be solved efficiently using standard optimization solvers?
• RQ4 To what extent does the proposed method improve fairness without sacrificing predictive accuracy?
• RQ5 Does the expected hinge loss serve as a valid upper bound on the misclassification probability in this setting?

Key findings

• The proposed model is equivalent to a mixed-binary optimization problem, enabling solution via standard solvers.
• The expectation of the hinge loss provides an upper bound on the misclassification probability.
• The worst-case unfairness measure is exactly reformulated using the ∞-Wasserstein ambiguity set.
• Numerical results show improved fairness with negligible loss in predictive accuracy.
• The method effectively enforces fairness under distributional uncertainty while maintaining robustness.