Age Optimal Sampling for Unreliable Channels under Unknown Channel Statistics
This addresses timeliness optimization in networked systems like IoT or communication networks, but it is incremental as it builds on existing AoI frameworks with unknown statistics.
The paper tackles the problem of minimizing Age of Information (AoI) for status updates over unreliable channels with unknown delay statistics by proposing an online learning algorithm, achieving a cumulative AoI regret rate of O(ln K) and proving it is minimax order optimal.
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 $Ω(\ln K)$ 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.