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Metric elicitation is a recent framework for eliciting classificationperformance metrics that best reflect implicit user preferences based on thetask and context. However, available elicitation strategies have been limitedto linear (or quasi-linear) functions of predictive rates, which can bepractically restrictive for many applications including fairness. This paperdevelops a strategy for eliciting more flexible multiclass metrics defined byquadratic functions of rates, designed to reflect human preferences better. Weshow its application in eliciting quadratic violation-based group-fair metrics.Our strategy requires only relative preference feedback, is robust to noise,and achieves near-optimal query complexity. We further extend this strategy toeliciting polynomial metrics -- thus broadening the use cases for metricelicitation.

Quadratic Metric Elicitation for Fairness and Beyond