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 beyond 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：信源动态、不可靠信道与信息陈旧性之间的复杂交互，长期以来被视为接收端实现准确、及时且最重要的面向目标决策的关键障碍。因此，诸如"信息年龄"、"信息价值"和"均方误差"等众多极具前景的指标应运而生，用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面向目标决策的效用。然而，迄今为止，尚未有指标被专门设计用来评估面向目标决策过程的效用。为此，本文研究了一种新颖的性能指标——面向目标的张量，以直接量化语义失配对面向目标决策的影响。基于GoT，我们考虑一个采样器-决策者配对，通过协作与分布式方式共同实现通信的共享目标。我们构建了一个无限时域的分散式部分可观测马尔可夫决策过程，以联合推导最优确定性采样策略与决策策略。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及其变体的文献成果，这标志着稀疏采样器与面向目标决策者联合设计的显著成就。