Age Optimal Sampling for Unreliable Channels under Unknown Channel Statistics

TL;DR

This paper develops an online learning algorithm to minimize the Age of Information in a system with unreliable channels and unknown delay statistics, achieving near-optimal regret bounds.

Contribution

It introduces a Robbins-Monro based online sampling policy that adapts to unknown channel delays and proves its near-optimal regret growth rate.

Findings

The proposed algorithm achieves $ ilde{O}( ext{ln} K)$ regret growth.

The algorithm is minimax order optimal with $ ilde{ ext{O}}( ext{ln} K)$ regret.

Simulation results confirm the effectiveness of the online learning approach.

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.