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.

在线校准的自适应风险控制 (ARC) 是一种基于集合预测的在线校准策略，提供最坏情况下确定性的长期风险控制以及统计边际覆盖保证。本文介绍了局部自适应风险控制 (L-ARC)，这是一种针对统计局部风险保证（从条件风险到边际风险）的在线校准方案，同时保持了 ARC 的最坏情况下的性能。L-ARC 在重构核希尔伯特空间 (RKHS) 中更新阈值函数，其中核函数确定了统计风险保证的局部化程度。理论结果显示了统计风险局部化与长期风险目标收敛速度之间的权衡。通过实验表明，由于局部化，L-ARC 能够在不同的数据子种群之间产生具有风险保证的预测集，从而显著提高了用于图像分割和无线网络中的波束选择等任务的校准模型的公平性。