Optimizations premised on open-loop metrics such as Age of Information (AoI) indirectly enhance the system's decision-making utility. We therefore propose a novel closed-loop metric named Goal-oriented Tensor (GoT) to directly quantify the impact of semantic mismatches on goal-oriented decision-making utility. Leveraging the GoT, we consider a sampler & decision-maker pair that works collaboratively and distributively to achieve a shared goal of communications. We formulate a two-agent infinite-horizon Decentralized Partially Observable Markov Decision Process (Dec-POMDP) to conjointly deduce the optimal deterministic sampling policy and decision-making policy. To circumvent the curse of dimensionality in obtaining an optimal deterministic joint policy through Brute-Force-Search, a sub-optimal yet computationally efficient algorithm is developed. This algorithm is predicated on the search for a Nash Equilibrium between the sampler and the decision-maker. Simulation results reveal that the proposed 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 progress in the semantics-conscious, goal-driven sparse sampling design.

翻译：基于信息年龄（AoI）等开环度量的优化间接提升了系统的决策效用。为此，我们提出一种新型闭环度量——面向目标的张量（GoT），以直接量化语义不匹配对面向目标决策效用的影响。借助GoT，我们考虑一对协作且分布式工作的采样器与决策器，共同实现通信的共享目标。我们构建了一个双智能体无限时域分散式部分可观测马尔可夫决策过程（Dec-POMDP），以联合推导最优确定性采样策略和决策策略。为规避通过暴力搜索获取最优确定性联合策略时的维度灾难，我们开发了一种次优但计算高效的算法。该算法基于在采样器与决策器之间搜索纳什均衡。仿真结果表明，所提出的采样器与决策器联合设计在目标达成效用与稀疏采样率方面均优于现有AoI及其变体相关文献，标志着语义感知、目标驱动的稀疏采样设计取得了进展。