Using Property Elicitation to Understand the Impacts of Fairness Regularizers

TL;DR

This paper investigates how regularizers influence the optimal solutions of predictive algorithms, especially in fairness contexts, using property elicitation to understand the conditions under which solutions change.

Contribution

It introduces a necessary and sufficient condition for when regularizers alter the optimal property, advancing understanding of regularizer impacts in fair machine learning.

Findings

Identifies conditions under which regularizers change the optimal property.

Demonstrates how decision-making varies with data distribution and constraint hardness.

Analyzes standard fairness regularizers in this framework.

Abstract

Predictive algorithms are often trained by optimizing some loss function, to which regularization functions are added to impose a penalty for violating constraints. As expected, the addition of such regularization functions can change the minimizer of the objective. It is not well-understood which regularizers change the minimizer of the loss, and, when the minimizer does change, how it changes. We use property elicitation to take first steps towards understanding the joint relationship between the loss and regularization functions and the optimal decision for a given problem instance. In particular, we give a necessary and sufficient condition on loss and regularizer pairs for when a property changes with the addition of the regularizer, and examine some regularizers satisfying this condition standard in the fair machine learning literature. We empirically demonstrate how algorithmic decision-making changes as a function of both data distribution changes and hardness of the constraints.