Empirical Risk Minimization under Fairness Constraints (1802.08626v3)

Abstract: We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.

Empirical Risk Minimization Under Fairness Constraints

The paper "Empirical Risk Minimization Under Fairness Constraints" explores the escalating challenge of ensuring fairness in machine learning models, particularly classifiers, in light of sensitive variables that might skew their outputs unjustly. The authors propose an enhancement to the traditional Empirical Risk Minimization (ERM) framework, integrating fairness constraints to stabilize the influence of sensitive variables on the conditional risk of the classifier. This is predicated on the understanding that models should not manifest disparate positive classification rates across diverse sensitive groups.

Methodological Contributions

1. Fair Empirical Risk Minimization (FERM): The core methodological innovation is the augmentation of the ERM framework to incorporate fairness constraints, formulated to minimize risk while ensuring equitable treatment of sensitive groups. The model seeks configurations where the classifier's positive prediction rates remain roughly constant across these groups.
2. Theoretical Foundations: The paper extends a statistical framework to derive both risk and fairness bounds, which authenticate the consistency of the approach. The authors lay out conditions under which their proposed method remains statistically reliable, offering a theoretical reassurance of its applicability in controlled settings.
3. Kernel Methods and Orthogonality Constraints: A notable insight is that fairness in the context of kernel methods translates into an orthogonality constraint between the classifier's decision boundary and the sensitive features vector. For linear classifiers, the fairness constraint simplifies to a preprocessing step that adjusts the data representation, maintaining standard machine learning practices while implicitly enforcing fairness.
4. Empirical Evaluation: The efficacy of the proposed method is empirically validated against state-of-the-art fairness approaches. This is underscored by experiments over multiple datasets using both linear and nonlinear models, with results exemplifying the method’s superior performance in four out of five datasets and competitive performance on the fifth.

Numerical Results and Empirical Finding

Experiments illuminate the effectiveness of FERM, demonstrating that the method maintains robust classification performance while offering improved fairness outcomes compared to baseline models. Significant claims arise from these experiments:

• FERM improves fairness (measured in DEO - Difference of Equal Opportunity) significantly without severely compromising overall accuracy.
• When applied to kernel methods like Support Vector Machines, the method elegantly integrates the fairness constraint, leading to superior empirical results on multiple datasets.

Implications and Future Directions

The proposed framework offers both theoretical and practical implications. Theoretically, it broadens the understanding of fairness in machine learning, giving mathematical credence to its integration within ERM. Practically, it offers a methodological template that can be adapted and expanded upon for diverse fairness-sensitive contexts, such as multi-class classification or regression.

The research also bifurcates potential exploration paths; one might examine alternative relaxations of fairness constraints beyond the linear and hinge loss functions exploited here. Furthermore, understanding how variations in the main fairness parameter ($\epsilon$) affect the trade-offs between model accuracy and fairness, and developing optimal strategies for such trade-offs, remains an enticing topic moving forward.

In conclusion, this work stands as a significant step in marrying classical machine learning objectives with emergent fairness considerations, fostering models that are not only effective but also equitable. As AI systems increasingly impact socio-economic decisions, such research is pivotal in ensuring ethical and just algorithmic practices.