We study a setting where an intelligent model (e.g., a pre-trained neural network) infers the real-time value of a target signal using data samples transmitted from a remote source. The transmission scheduler decides (i) the freshness of packets, (ii) their length (i.e., the number of samples they contain), and (iii) when they should be transmitted. The freshness is quantified using the Age of Information (AoI), and the inference quality for a given packet length is a general function of AoI. Previous works assumed i.i.d. transmission delays with immediate feedback or were restricted to the case where inference performance degrades as the input data ages. Our formulation, in addition to capturing non-monotone age dependence, also covers Markovian delay on both forward and feedback links. We model this as an infinite-horizon average-cost Semi-Markov Decision Process. We obtain a closed-form solution that decides on (i) and (iii) for any constant packet length. The solution for when to transmit is an index-based threshold policy, where the index function is expressed in terms of the delay state and AoI at the receiver. In contrast, the freshness of the selected packet is a function of only the delay state. We then separately optimize the value of the constant packet length. Moreover, we also develop an index-based threshold policy for the time-variable packet length case, which allows a complexity reduction. In simulation results, we observe that our goal-oriented scheduler drops inference error down to one-sixth with respect to the age-based scheduling of unit-length packets.

翻译：本文研究一种智能模型（例如预训练神经网络）利用远程源传输的数据样本来推断目标信号实时值的场景。传输调度器需决策：（i）数据包的新鲜度，（ii）数据包长度（即包含的样本数量），以及（iii）数据包的发送时机。新鲜度采用信息年龄（AoI）进行量化，给定包长下的推断质量是AoI的广义函数。先前研究假设传输延迟为独立同分布且具有即时反馈，或仅限于推断性能随输入数据老化而下降的情况。我们的模型不仅捕捉了非单调的年龄依赖性，还涵盖了前向与反馈链路的马尔可夫延迟特性。我们将此建模为无限时域平均成本半马尔可夫决策过程。针对任意恒定包长，我们获得了决策（i）和（iii）的闭式解。其中发送时机的决策表现为基于指标的阈值策略，指标函数由接收端的延迟状态与AoI表示；而所选数据包的新鲜度仅取决于延迟状态。随后，我们单独优化了恒定包长的取值。此外，针对时变包长场景，我们还提出了一种基于指标的阈值策略，可有效降低计算复杂度。仿真结果表明，相较于基于年龄的单元包长调度策略，我们的目标导向调度器能将推断误差降低至其六分之一。