Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading

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.