From Freshness to Effectiveness: Goal-Oriented Sampling for Remote Decision Making

Abstract: Data freshness, measured by Age of Information (AoI), is highly relevant in networked applications such as Vehicle to Everything (V2X), smart health systems, and Industrial Internet of Things (IIoT). Yet, freshness alone does not equate to informativeness. In decision-critical settings, some stale data may prove more valuable than fresh updates. To explore this nuance, we move beyond AoI-centric policies and investigate how data staleness impacts decision-making under data-staleness-induced uncertainty. We pose a central question: What is the value of information, when freshness fades, and only its power to shape remote decisions remains? To capture this endured value, we propose AR-MDP, an Age-aware Remote Markov Decision Process framework, which co-designs optimal sampling and remote decision-making under a sampling frequency constraint and random delay. To efficiently solve this problem, we design a new two-stage hierarchical algorithm namely Quick Bellman-Linear-Program (QuickBLP), where the first stage involves solving the Dinkelbach root of a Bellman variant and the second stage involves solving a streamlined linear program (LP). For the tricky first stage, we propose a new One-layer Primal-Dinkelbach Synchronous Iteration (OnePDSI) method, which overcomes the re-convergence and non-expansive divergence present in existing per-sample multi-layer algorithms. Through rigorous convergence analysis of our proposed algorithms, we establish that the worst-case optimality gap in OnePDSI exhibits exponential decay with respect to iteration $K$ at a rate of $\mathcal{O}(\frac{1}{R^K})$. Through sensitivity analysis, we derive a threshold for the sampling frequency, beyond which additional sampling does not yield further gains in decision-making. Simulation results validate our analyses.