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In this work, we study a status update system with a source node sendingtimely information to the destination through a channel with random delay. Wemeasure the timeliness of the information stored at the receiver via the Age ofInformation (AoI), the time elapsed since the freshest sample stored at thereceiver is generated. The goal is to design a sampling strategy that minimizesthe total cost of the expected time average AoI and sampling cost in theabsence of transmission delay statistics. We reformulate the total costminimization problem as the optimization of a renewal-reward process, andpropose an online sampling strategy based on the Robbins-Monro algorithm.Denote $K$ to be the number of samples we have taken. We show that, when thetransmission delay is bounded, the expected time average total cost obtained bythe proposed online algorithm converges to the minimum cost when $K$ goes toinfinity, and the optimality gap decays with rate $\mathcal{O}\left(\lnK/K\right)$. Simulation results validate the performance of our proposedalgorithm.

Sending Timely Status Updates through Channel with Random Delay via Online Learning