Using Property Elicitation to Understand the Impacts of Fairness Regularizers
This work addresses a foundational gap in fair machine learning by clarifying the impact of regularization, which is incremental but important for algorithm design.
The paper tackles the problem of understanding how fairness regularizers affect the optimal decisions in predictive algorithms, providing a necessary and sufficient condition for when regularizers change the minimizer and empirically showing how decisions vary with data distribution and constraint hardness.
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.