The intricate interplay of source dynamics, unreliable channels, and staleness of information has long been recognized as a significant impediment for the receiver to achieve accurate, timely, and most importantly, goal-oriented decision making. Thus, a plethora of promising metrics, such as Age of Information, Value of Information, and Mean Square Error, have emerged to quantify these underlying adverse factors. Following this avenue, optimizing these metrics has indirectly improved the utility of goal-oriented decision making. Nevertheless, no metric has hitherto been expressly devised to evaluate the utility of a goal-oriented decision-making process. To this end, this paper investigates a novel performance metric, the Goal-oriented Tensor (GoT), to directly quantify the impact of semantic mismatches on the goal-oriented decision making. Based on the GoT, we consider a sampler-decision maker pair that work collaboratively and distributively to achieve a shared goal of communications. We formulate an infinite-horizon Decentralized Partially Observable Markov Decision Process (Dec-POMDP) to conjointly deduce the optimal deterministic sampling policy and decision-making policy. The simulation results reveal that the sampler-decision maker co-design surpasses the current literature on AoI and its variants in terms of both goal achievement utility and sparse sampling rate, signifying a notable accomplishment for a sparse sampler and goal-oriented decision maker co-design.

翻译：源动态、不可靠信道和信息陈旧度的复杂相互作用，长期以来被认为是接收方实现准确、及时且最重要的是目标导向决策的重大障碍。因此，诸如信息年龄、信息价值和均方误差等大量有前景的指标应运而生，以量化这些潜在的不利因素。沿着这一方向，优化这些指标间接提升了目标导向决策的效用。然而，迄今为止尚未有指标被专门设计用于评估目标导向决策过程的效用。为此，本文研究了一种新颖的性能指标——面向目标的张量，以直接量化语义不匹配对目标导向决策的影响。基于GoT，我们考虑一个采样器-决策者对，它们协作且分布式地工作，以实现共同的通信目标。我们构建了一个无限时域的分散部分可观察马尔可夫决策过程来联合推导最优确定性采样策略和决策策略。仿真结果表明，采样器-决策者联合设计在目标达成效用和稀疏采样率方面均超越了当前关于AoI及其变体的文献，标志着稀疏采样器与目标导向决策者联合设计的重要成就。