Age Optimal Sampling for Unreliable Channels Under Unknown Channel Statistics.

In this work, we study a system with a sensor forwarding status update to the receiver through an error-prone channel, and the receiver sends the transmission results to the sensor via a reliable link. We assume both transmission links suffer from random delays. We use Age of Information (AoI) to measure the freshness of the status information at the receiver. Our goal is to design a sampling policy that minimizes the expected time average AoI when the channel statistics are unknown. The problem is reformulated into a renewal-reward process optimization, and an online algorithm based on the Robbins-Monro algorithm is proposed. We prove that when the forward and backward transmission delays are bounded, the AoI difference between the online algorithm and the optimal policy decays with rate $\mathcal{O}(\ln K/K)$ , where $K$ is the number of successful transmissions. Simulation results validate the performance of our proposed algorithm.