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.

翻译：自适应风险控制（ARC）是一种基于集预测的在线校准策略，能够在最坏情况下实现确定性长期风险控制，并提供统计边际覆盖保证。ARC通过根据过去决策的反馈调整单一标量阈值来改变预测集的大小。在本工作中，我们提出局部自适应风险控制（L-ARC），这是一种针对从条件风险到边际风险的统计局部风险保证的在线校准方案，同时保留了ARC的最坏情况性能。L-ARC在再生核希尔伯特空间（RKHS）内更新阈值函数，其中核函数决定统计风险保证的局部化程度。理论结果突显了统计风险局部化与收敛到长期风险目标速度之间的权衡。得益于局部化，实验证明L-ARC能够为不同数据子群体生成具有风险保证的预测集，显著提升了校准模型在图像分割和无线网络波束选择等任务中的公平性。