Age Optimal Sampling for Unreliable Channels under Unknown Channel Statistics

2024-12-24

arXiv.org

AI Summary

This paper addresses the problem of adaptively designing sampling policies to minimize the average Age of Information (AoI) in status-updating systems where channel statistics—particularly the delay distribution—are unknown and transmissions are unreliable. Specifically, it considers a dual-uncertainty setting: (i) reliable but randomly delayed feedback at the receiver, and (ii) error-prone uplink channels with unknown delay distributions at the sensor. To this end, the AoI optimization is first formulated as a stochastic approximation problem under unknown delay distributions. A Robbins–Monro-type online algorithm with momentum is proposed, which converges almost surely to the optimal threshold-based policy. Theoretically, the algorithm achieves an $O(ln K)$ upper bound on cumulative AoI regret over $K$ epochs, matching the $Omega(ln K)$ minimax lower bound—establishing order optimality. Extensive simulations demonstrate that the proposed algorithm significantly outperforms baseline strategies across diverse delay distributions.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper, we study a system in which a sensor forwards status updates to a receiver through an error-prone channel, while the receiver sends the transmission results back to the sensor via a reliable channel. Both channels are subject to random delays. To evaluate the timeliness of the status information at the receiver, we use the Age of Information (AoI) metric. The objective is to design a sampling policy that minimizes the expected time-average AoI, even when the channel statistics (e.g., delay distributions) are unknown. We first review the threshold structure of the optimal offline policy under known channel statistics and then reformulate the design of the online algorithm as a stochastic approximation problem. We propose a Robbins-Monro algorithm to solve this problem and demonstrate that the optimal threshold can be approximated almost surely. Moreover, we prove that the cumulative AoI regret of the online algorithm increases with rate $mathcal{O}(ln K)$, where $K$ is the number of successful transmissions. In addition, our algorithm is shown to be minimax order optimal, in the sense that for any online learning algorithm, the cumulative AoI regret up to the $K$-th successful transmissions grows with the rate at least $Omega(ln K)$ in the worst case delay distribution. Finally, we improve the stability of the proposed online learning algorithm through a momentum-based stochastic gradient descent algorithm. Simulation results validate the performance of our proposed algorithm.

Problem

• Minimize Age of Information in unreliable channels
• Design sampling policy with unknown channel statistics
• Propose online algorithm for optimal threshold approximation

Innovation

• Robbins-Monro algorithm
• minimax order optimal
• momentum-based stochastic gradient