We study the design of a goal-oriented sampling and scheduling strategy through a channel with highly variable two-way random delay, which can exhibit memory (e.g., Delay and Disruption Tolerant Networks). The objective of the communication is to optimize the performance of remote inference, where an inference algorithm (e.g., a trained neural network) on the receiver side predicts a time-varying target signal using the data samples transmitted by a sensor. Previous formulations to this problem either assumed a channel with IID transmission delay, neglecting feedback delay, or considered the monotonic relation that the performance only gets worse as the input information ages. We show how, with delayed feedback, one can effectively exploit the knowledge about delay memory through an index-based threshold policy. This policy minimizes the expected time-average inference error that can be monotone or non-monotone in age. The index function is expressed in terms of the Age of Information (AoI) on the receiver side and a parameter regarding the distribution of subsequent transmission delay, both of which can readily be tracked.

翻译：我们研究了一种通过具有高度可变双向随机延迟（可能表现出记忆性，例如，延迟和中断容忍网络）的信道设计目标导向采样与调度策略的问题。通信的目标是优化远程推断的性能，其中接收端的推断算法（例如，训练好的神经网络）使用传感器传输的数据样本来预测时变目标信号。先前针对该问题的公式要么假设信道具有独立同分布传输延迟，忽略反馈延迟，要么考虑输入信息老化时性能只会变差的单调关系。我们展示了如何利用延迟反馈，通过基于索引的阈值策略有效利用关于延迟记忆的知识。该策略最小化了期望时间平均推断误差，该误差可能在年龄上呈现单调或非单调性。索引函数表示为接收端的信息年龄（AoI）和关于后续传输延迟分布的参数，这两个参数均可轻松追踪。