边云协同下在线校准线性求解不确定性，保障长期覆盖精度
Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading
- 基于在线置信预测校准概率解集的置信阈值
- 在有限计算资源下实现95%以上长期覆盖率
- 适合对可靠性要求高的边缘计算场景
在边缘计算场景中，用户向计算能力波动的边缘处理器提交线性系统求解请求。边缘端采用概率线性求解器（PLS）以在时限和预算内响应，输出一组可能解。由于模型误设，直接使用PLS得到的高概率密度（HPD）集合无法保证对真实解的覆盖率。本文提出在线置信预测-概率线性求解器（OCP-PLS），通过间歇性云端反馈，在线校准不确定度阈值。该方法利用在线置信预测（OCP）实现动态优化，确保长期覆盖率。实验验证了方法有效性，并揭示了覆盖率、预测集大小与云端使用频率之间的权衡关系。
原文摘要 · Abstract (English)
Consider an edge computing setting in which a user submits queries for the solution of a linear system to an edge processor, which is subject to time-varying computing availability. The edge processor applies a probabilistic linear solver (PLS) so as to be able to respond to the user's query within the allotted time and computing budget. Feedback to the user is in the form of a set of plausible solutions. Due to model misspecification, the highest-probability-density (HPD) set obtained via a direct application of PLS does not come with coverage guarantees with respect to the true solution of the linear system. This work introduces a new method to calibrate the HPD sets produced by PLS with the aim of guaranteeing long-term coverage requirements. The proposed method, referred to as online conformal prediction-PLS (OCP-PLS), assumes sporadic feedback from cloud to edge. This enables the online calibration of uncertainty thresholds via online conformal prediction (OCP), an online optimization method previously studied in the context of prediction models. The validity of OCP-PLS is verified via experiments that bring insights into trade-offs between coverage, prediction set size, and cloud usage.
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