Localized Adaptive Risk Control
This work addresses fairness issues in machine learning by enhancing risk control for specific subpopulations, representing an incremental advancement over existing adaptive risk control methods.
The paper tackles the problem of providing statistical localized risk guarantees in online calibration, introducing Localized Adaptive Risk Control (L-ARC) to improve fairness across data subpopulations, with experiments showing significant improvements in tasks like image segmentation and beam selection.
Adaptive Risk Control (ARC) is an online calibration strategy based on set prediction that offers worst-case deterministic long-term risk control, as well as statistical marginal coverage guarantees. ARC adjusts the size of the prediction set by varying a single scalar threshold based on feedback from past decisions. In this work, we introduce Localized Adaptive Risk Control (L-ARC), an online calibration scheme that targets statistical localized risk guarantees ranging from conditional risk to marginal risk, while preserving the worst-case performance of ARC. L-ARC updates a threshold function within a reproducing kernel Hilbert space (RKHS), with the kernel determining the level of localization of the statistical risk guarantee. The theoretical results highlight a trade-off between localization of the statistical risk and convergence speed to the long-term risk target. Thanks to localization, L-ARC is demonstrated via experiments to produce prediction sets with risk guarantees across different data subpopulations, significantly improving the fairness of the calibrated model for tasks such as image segmentation and beam selection in wireless networks.