Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading

TL;DR

This work tackles reliable, low-latency linear system solving in edge–cloud settings by calibrating probabilistic linear solvers (PLS) with online conformal prediction (OCP). By defining an score-based HPD set and integrating sporadic cloud feedback, the proposed OCP-PLS guarantees long-term coverage of the true solution while adapting cloud usage to budgeted edge computation. Theoretical results establish a finite-time bound on the deviation from the target coverage, and experiments demonstrate that OCP-PLS achieves similar HPD sizes to full-feedback methods while substantially reducing cloud communication, even under time-varying budgets. The approach advances practical reliability in PN-based numerical solvers for resource-constrained, dynamic networks, with potential extensions to other numerical problems beyond linear systems.

Abstract

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.

Figures (4)

• Figure 1: At each round $t$, a user submits a linear system defined by the pair $(A_t, b_t)$ to an edge device. Given the available computing budget $I_t$, the edge device employs a probabilistic linear solver (PLS), obtaining a highest-probability-density (HPD) set $\mathcal{C}_t$ for the true solution $x^*_t = A_t^{-1}b_t$. The set $\mathcal{C}_t$ is returned in a timely fashion to the user. The proposed method, OCP-PLS ensures long-term coverage guarantees (\ref{['eq:coverage_guarantee']}) for the HPD sets $\mathcal{C}_t$, addressing model misspecification in PLS. To this end, OCP-PLS allows for sporadic communication between cloud and edge.
• Figure 2: Timeline of messages exchanged across cloud, edge, and user.
• Figure 3: Coverage (a), set size (b), and cumulative cloud-to-edge feedback rate (c) for PLS, OCP-PLS, and OCP-PLS with full cloud-to-edge feedback for target coverage level $1-\alpha = 0.9$ (red dashed line in (a)). The gray dashed line in (a) corresponds to the threshold bound (\ref{['eq:guarantee_iocp']}).
• Figure 4: Coverage (a), set size (b), and cumulative cloud-to-edge feedback rate (c) for PLS, OCP-PLS, and OCP-PLS with full cloud-to-edge feedback for target coverage level $1-\alpha = 0.9$ (red dashed line in (a)) in a setting with time-varying edge computing budget. The gray dashed line in (a) corresponds to the threshold bound (\ref{['eq:guarantee_iocp']}).

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof