Online Learning of Goal-Oriented Status Updating With Unknown Delay Statistics

With the proliferation of communication demand, goal-oriented communication goes beyond traditional bit-level approaches by emphasizing the significance of information and its relevance to specific goals. This paper addresses the goal-oriented status updating problem, where detecting status changes is crucial. We employ the Age of Changed Information (AoCI) as a metric, which considers both the timeliness and content of the update. Our goal is to minimize the weighted sum of AoCI and transmission cost without channel delay statistics. The investigated problem is formulated as a semi-Markov decision process (SMDP) and is tackled by converting it into a multi-variable optimization problem. We prove that the optimal updating policy is of threshold type, and derive a nearly closed-form expression for the optimal threshold. When delay statistics are available, the optimal threshold can be obtained by a bisection searching algorithm. In the absence of prior delay statistics, we develop an online learning policy. We demonstrate that the optimality gap decays at a rate of $\mathcal {O}(\log K / K)$ , where K is the number of samples. Simulation results are presented to compare the performance of various policies under different statistical conditions, showcasing the superiority of our proposed algorithm.