Quadratic Metric Elicitation for Fairness and Beyond

Metric elicitation is a recent framework for eliciting performance metrics that best reflect implicit user preferences based on the application and context. However, available elicitation strategies have been limited to linear (or quasi-linear) functions of predictive rates, which can be practically restrictive for many domains including fairness. This paper develops a strategy for eliciting more flexible multiclass metrics defined by quadratic functions of rates, designed to reflect human preferences better. We show its application in eliciting quadratic violation-based group-fair metrics. Our strategy requires only relative preference feedback, and that too of near-optimal amount, and is robust to feedback noise. We further extend this strategy to eliciting polynomial metrics -- thus broadening the use cases for metric elicitation.