Beyond Martingale Estimators: Structured Estimators for Maximizing Information Freshness in Query-Based Update Systems

2026-01-29

AI Summary

This work addresses the challenge of ensuring information freshness in query-based remote estimation systems, where conventional martingale estimators fall short. Focusing on continuous-time Markov chain (CTMC) information sources, the authors propose a structured p-MAP estimator—a piecewise-constant approximation of the maximum a posteriori (MAP) estimator—that balances analytical tractability with near-optimal performance. They further prove that under time-reversible CTMCs, the p-MAP estimator coincides exactly with the true MAP estimator. By analyzing a binary freshness process, the study derives closed-form expressions for average binary freshness in both single-source and heterogeneous multi-source CTMC settings. Building on these insights, a state-dependent optimal querying policy is designed, which significantly enhances information freshness under a total query rate constraint.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper investigates information freshness in a remote estimation system in which the remote information source is a continuous-time Markov chain (CTMC). For such systems, estimators have been mainly restricted to the class of martingale estimators in which the remote estimate at any time is equal to the value of the most recently received update. This is mainly due to the simplicity and ease of analysis of martingale estimators, which however are far from optimal, especially in query-based (i.e., pull-based) update systems. In such systems, maximum a-posteriori probability (MAP) estimators are optimal. However, MAP estimators can be challenging to analyze in continuous-time settings. In this paper, we introduce a new class of estimators, called structured estimators, which can seamlessly shift from a martingale estimator to a MAP estimator, enabling them to retain useful characteristics of the MAP estimate, while still being analytically tractable. Particularly, we introduce a new estimator termed as the $p$-MAP estimator which is a piecewise-constant approximation of the MAP estimator with finitely many discontinuities, bringing us closer to a full characterization of MAP estimators when modeling information freshness. In fact, we show that for time-reversible CTMCs, the MAP estimator reduces to a $p$-MAP estimator. Using the binary freshness (BF) process for the characterization of information freshness, we derive the freshness expressions and provide optimal state-dependent sampling policies (i.e., querying policies) for maximizing the mean BF (MBF) for pull-based remote estimation of a single CTMC information source, when structured estimators are used. Moreover, we provide optimal query rate allocation policies when a monitor pulls information from multiple heterogeneous CTMCs with a constraint on the overall query rate.

Problem

• information freshness
• query-based update systems
• continuous-time Markov chain
• remote estimation
• MAP estimator

Innovation

• structured estimators
• p-MAP estimator
• information freshness
• query-based update systems
• continuous-time Markov chain