Multi-Stage Structured Estimators for Information Freshness

TL;DR

This paper introduces a new class of multi-stage estimators called p-MAP estimators that better approximate optimal MAP estimators for information freshness in pull-based systems, addressing limitations of traditional martingale estimators.

Contribution

The paper proposes p-MAP estimators as a novel approach to model MAP estimators as piecewise constant functions with multiple stages, enhancing analysis of information freshness.

Findings

p-MAP estimators effectively approximate MAP estimators.

Multi-stage structure improves analysis of information freshness.

Addresses limitations of martingale estimators in pull-based 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.