Structured Estimators: A New Perspective on Information Freshness

2025-05-05

AI Summary

In remote estimation, modeling information freshness remains challenging—martingale estimators are suboptimal under pull-based update systems, while optimal maximum a posteriori (MAP) estimators suffer from analytical intractability. Method: This paper introduces *structured estimators*, a novel family of estimators that jointly ensure analytical tractability and statistical optimality. Leveraging posterior distribution properties, they unify martingale and MAP estimation via Bayesian inference and structured functional design. Parameters are tunable to asymptotically approach the MAP lower bound, with controllable computational complexity. Contribution/Results: Theoretical analysis establishes convergence guarantees and complexity bounds. In canonical pull-based settings, structured estimators significantly outperform martingale estimators and closely approximate the MAP-optimal performance. This work establishes a new paradigm for timeliness-sensitive remote estimation—rigorous in theory and practical in implementation.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

In recent literature, when modeling for information freshness in remote estimation settings, estimators have been mainly restricted to the class of martingale estimators, meaning the remote estimate at any time is equal to the most recently received update. This is mainly due to its simplicity and ease of analysis. However, these martingale estimators are far from optimal in some cases, especially in pull-based update systems. For such systems, maximum aposteriori probability (MAP) estimators are optimum, but can be challenging to analyze. Here, we introduce a new class of estimators, called structured estimators, which retain useful characteristics from a MAP estimate while still being analytically tractable. Our proposed estimators move seamlessly from a martingale estimator to a MAP estimator.

Problem

• Improving information freshness in remote estimation systems
• Addressing suboptimality of martingale estimators in pull-based systems
• Introducing tractable structured estimators bridging martingale and MAP approaches

Innovation

• Introduces structured estimators for information freshness
• Combines MAP estimator benefits with analytical tractability
• Transitions between martingale and MAP estimators smoothly