[Paper Review] Fairness risk measures

Robert C. Williamson, Aditya Krishna Menon|arXiv (Cornell University)|May 24, 2019

Health Systems, Economic Evaluations, Quality of Life29 citations

TL;DR

This paper proposes a new fairness definition that ensures commensurate expected losses across subgroups defined by sensitive features, generalizing prior work to handle categorical and real-valued sensitive attributes. By linking fairness to risk measures from mathematical finance, it introduces a convex optimization objective based on conditional value at risk (CVaR), enabling efficient and scalable fair learning with strong theoretical guarantees.

ABSTRACT

Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either binary sensitive features (thus precluding categorical or real-valued sensitive groups), or result in non-convex objectives (thus adversely affecting the optimisation landscape). In this paper, we propose a new definition of fairness that generalises some existing proposals, while allowing for generic sensitive features and resulting in a convex objective. The key idea is to enforce that the expected losses (or risks) across each subgroup induced by the sensitive feature are commensurate. We show how this relates to the rich literature on risk measures from mathematical finance. As a special case, this leads to a new convex fairness-aware objective based on minimising the conditional value at risk (CVaR).

Motivation & Objective

• To address the limitations of existing fairness definitions that are restricted to binary sensitive features or lead to non-convex optimization problems.
• To develop a fairness definition that generalizes existing proposals while supporting generic sensitive features, including categorical and real-valued groups.
• To formulate a convex optimization objective for fairness-aware learning, improving tractability and scalability in practice.
• To connect fairness in machine learning to the established theory of risk measures from mathematical finance.
• To demonstrate that minimizing conditional value at risk (CVaR) of subgroup risks yields a convex, scalable, and theoretically grounded fairness objective.

Proposed method

• Proposes a fairness definition based on equalizing expected losses (risks) across subgroups induced by sensitive features, ensuring commensurability.
• Frames the fairness constraint within the mathematical finance framework of risk measures, particularly conditional value at risk (CVaR).
• Derives a convex optimization objective by minimizing the CVaR of the loss distribution across sensitive subgroups.
• Applies the proposed framework to supervised learning tasks, enabling end-to-end training with fairness constraints.
• Demonstrates that the resulting optimization problem is convex, ensuring global convergence and efficient computation.
• Generalizes prior fairness definitions by allowing arbitrary sensitive features, including continuous and multi-class attributes.

Experimental results

Research questions

• RQ1 How can fairness be defined in a way that applies to arbitrary sensitive features, including categorical and real-valued groups?
• RQ2 Can a fairness objective be constructed that is both theoretically sound and computationally tractable?
• RQ3 What is the connection between fairness in machine learning and risk measures from mathematical finance?
• RQ4 Does minimizing CVaR of subgroup risks lead to a convex optimization problem suitable for scalable training?
• RQ5 How does the proposed fairness definition compare to existing definitions in terms of generalization and robustness?

Key findings

• The proposed fairness definition generalizes existing approaches by allowing any type of sensitive feature, including continuous and multi-class attributes.
• The method results in a convex optimization objective, enabling efficient and globally optimal training of fair classifiers.
• By linking fairness to risk measures, the approach inherits strong theoretical properties from mathematical finance.
• The use of CVaR as a fairness objective ensures that the worst-performing subgroup is prioritized, improving equity.
• The framework supports scalable training through convex optimization, making it practical for real-world applications.
• The approach subsumes and extends prior fairness definitions, such as equalized odds and equal opportunity, under a unified convex formulation.