AI 中文总结
本文针对在线共形预测的三类局限，提出统一在线学习框架，在对抗、全得分反馈随机、协变量依赖随机场景下，分别推导或建立同时满足覆盖与效率保证的方法及相关理论结果。
AI 中文摘要
Gibbs和Candès提出的自适应共形推理（ACI）及其变体是分布偏移下在线共形预测的标准方法，但存在三个根本局限：其一，其保证仅控制符号化的长期覆盖误差，某一方向的持续未覆盖误差会被后续补偿误差掩盖，导致方法满足理论保证却长期出错；其二，现有保证未提及预测集大小，可能以预测集过宽为代价 trivial 地实现有效性；其三，现有效率保证是与事后选定的固定预测器比较，数据生成分布偏移后该基准意义渐弱，最优阈值概念也随时间变化。本文考虑统一在线学习框架，针对三类重要模型同时控制绝对、不可抵消的覆盖违反及针对动态演化基准的预测集效率。在完全对抗场景下，利用标准ACI更新恰好是分位数损失上的投影在线梯度下降这一事实，推导任意单调Lipschitz效率目标的同时覆盖与效率保证，无分布或凸性假设；在全得分反馈的随机场景下，提出滑动窗口分位数跟踪器，建立匹配的极小极大下界，证明算法速率最优；在协变量依赖的随机场景下，开发分区ACI算法跟踪函数值神谕阈值，推导同时覆盖与效率保证。
英文摘要
Adaptive conformal inference (ACI) of Gibbs and Cand{è}s and its variants are the standard approach to online conformal prediction under distribution shift, but they suffer from three fundamental limitations. First, their guarantees control only the \emph{signed} long-run coverage error: persistent miscoverage in one direction can be masked by compensating errors later, so a method can satisfy the theoretical guarantee while being badly wrong for extended periods. Second, existing guarantees say nothing about prediction-set size, so validity can be achieved trivially at the cost of unduly wide prediction sets. Third, the efficiency guarantees that do exist compare against a \emph{fixed} predictor chosen in hindsight, a benchmark that becomes increasingly less meaningful once the data-generating distribution shifts, since the very notion of an optimal threshold then changes over time. We consider a unified online learning framework that simultaneously controls absolute, non-cancelling coverage violation and prediction-set efficiency against a dynamically evolving benchmark for three important models. In the fully adversarial setting, exploiting the fact that the standard ACI update is exactly projected online gradient descent on the pinball loss, we derive simultaneous coverage and efficiency guarantees for arbitrary monotone Lipschitz efficiency objectives, with no distributional or {\it convexity} assumptions. In the stochastic setting with full-score feedback, we propose a sliding-window quantile tracker and establish a matching minimax lower bound showing our algorithm is rate-optimal. In the covariate-dependent stochastic setting, we develop a partitioned ACI algorithm that tracks a function-valued oracle threshold, and derive simultaneous coverage and efficiency guarantees.
CommentsWe acknowledge the use of LLMs for editorial assistance in improving the clarity, style, proof checking, and figure generation of this manuscript
