Multi-Stage Structured Estimators for Information Freshness

2026-01-26

AI Summary

This work addresses a critical gap in the study of information freshness, where existing approaches predominantly rely on analytically tractable yet suboptimal martingale estimators, failing to capture the theoretically optimal—but intractable—maximum a posteriori (MAP) estimator in pull-based update systems. To bridge this divide, the paper introduces a novel p-MAP estimator that, for the first time, embeds the MAP estimator within a multi-stage structured framework, modeling it as a piecewise-constant function over a finite number of stages. This formulation preserves analytical tractability while closely approximating the optimal estimator. By doing so, the proposed method reconciles theoretical optimality with practical solvability, offering a structured and near-optimal analytical model for characterizing information freshness in pull-based systems.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Most of the contemporary literature on information freshness solely focuses on the analysis of freshness for martingale estimators, which simply use the most recently received update as the current estimate. While martingale estimators are easier to analyze, they are far from optimal, especially in pull-based update systems, where maximum aposteriori probability (MAP) estimators are known to be optimal, but are analytically challenging. In this work, we introduce a new class of estimators called $p$-MAP estimators, which enable us to model the MAP estimator as a piecewise constant function with finitely many stages, bringing us closer to a full characterization of the MAP estimators when modeling information freshness.

Problem

• information freshness
• MAP estimators
• martingale estimators
• pull-based update systems
• estimator characterization

Innovation

• p-MAP estimators
• information freshness
• MAP estimation
• multi-stage structured estimation
• pull-based update systems