We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

翻译：我们研究通过预测集进行不确定性量化的问题，其背景为在线设定下数据分布可能随时间任意变化。近期研究利用在线学习领域中的遗憾最小化算法开发了在线共形预测技术，能够学习具有近似有效覆盖率和较小遗憾的预测集。然而，标准遗憾最小化可能不足以应对动态变化的环境——这类场景不仅要求在完整时间跨度内保证性能，更需要在所有（子）时间区间内均能提供性能保障。我们提出新型在线共形预测方法，可最小化强自适应遗憾——该指标衡量固定长度所有区间上的最差情况遗憾。理论证明表明，我们的方法能同时在所有区间长度上实现接近最优的强自适应遗憾，并保证近似有效的覆盖率。实验显示，在时间序列预测与分布偏移下的图像分类等实际任务中，我们的方法相较现有方法始终能获得更优的覆盖率与更小的预测集。