Revisiting Reweighted Risk for Calibration: AURC, Focal Loss, and Inverse Focal Loss

Abstract: Several variants of reweighted risk functionals, such as focal losss, inverse focal loss, and the Area Under the Risk-Coverage Curve (AURC), have been proposed in the literature and claims have been made in relation to their calibration properties. However, focal loss and inverse focal loss propose vastly different weighting schemes. In this paper, we revisit a broad class of weighted risk functions commonly used in deep learning and establish a principled connection between these reweighting schemes and calibration errors. We show that minimizing calibration error is closely linked to the selective classification paradigm and demonstrate that optimizing a regularized variant of the AURC naturally leads to improved calibration. This regularized AURC shares a similar reweighting strategy with inverse focal loss, lending support to the idea that focal loss is less principled when calibration is a desired outcome. Direct AURC optimization offers greater flexibility through the choice of confidence score functions (CSFs). To enable gradient-based optimization, we introduce a differentiable formulation of the regularized AURC using the SoftRank technique. Empirical evaluations demonstrate that our AURC-based loss achieves competitive class-wise calibration performance across a range of datasets and model architectures.