In many real-world problems, predictions are leveraged to monitor and control cyber-physical systems, demanding guarantees on the satisfaction of reliability and safety requirements. However, predictions are inherently uncertain, and managing prediction uncertainty presents significant challenges in environments characterized by complex dynamics and forking trajectories. In this work, we assume access to a pre-designed probabilistic implicit or explicit sequence model, which may have been obtained using model-based or model-free methods. We introduce probabilistic time series-conformal risk prediction (PTS-CRC), a novel post-hoc calibration procedure that operates on the predictions produced by any pre-designed probabilistic forecaster to yield reliable error bars. In contrast to existing art, PTS-CRC produces predictive sets based on an ensemble of multiple prototype trajectories sampled from the sequence model, supporting the efficient representation of forking uncertainties. Furthermore, unlike the state of the art, PTS-CRC can satisfy reliability definitions beyond coverage. This property is leveraged to devise a novel model predictive control (MPC) framework that addresses open-loop and closed-loop control problems under general average constraints on the quality or safety of the control policy. We experimentally validate the performance of PTS-CRC prediction and control by studying a number of use cases in the context of wireless networking. Across all the considered tasks, PTS-CRC predictors are shown to provide more informative predictive sets, as well as safe control policies with larger returns.

翻译：在许多现实问题中，预测结果被用于监控和控制信息物理系统，要求满足可靠性和安全性的保证。然而预测本身具有内在不确定性，在复杂动态环境和分支轨迹场景中，管理预测不确定性面临重大挑战。本文假设可获取预先设计的概率隐式或显式序列模型（可能通过基于模型或无模型方法获得）。我们提出概率时间序列共形风险预测（PTS-CRC），这是一种新颖的事后校准方法，可对任意预设计概率预测器产生的预测结果进行操作，生成可靠的误差界限。与现有技术相比，PTS-CRC基于从序列模型中采样的多个原型轨迹集合生成预测集，有效支持分支不确定性的高效表征。此外，不同于现有方法，PTS-CRC能够满足超出覆盖范围的可靠性定义。该特性被用于设计新型模型预测控制（MPC）框架，在控制策略质量或安全性的一般平均约束下，解决开环与闭环控制问题。我们通过无线网络场景中的多个用例实验验证了PTS-CRC预测与控制的性能。在所有测试任务中，PTS-CRC预测器均能提供更具信息量的预测集，以及具有更大回报的安全控制策略。