Goal-Oriented Tensor: Beyond AoI Towards Semantics-Empowered Goal-Oriented Communications

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 goal-oriented decision making. Thus, a plethora of promising metrics, such as Age of Information and Value of Information have emerged to quantify these adverse factors. Optimizing these metrics indirectly improves the goal-oriented utility of decision making. Nevertheless, no metric has been devised to directly evaluate the utility. To this end, this paper investigates a novel tensor-based metric, named Goal-oriented Tensor (GoT), to directly quantify the impact of semantic mismatches on decision making. Leveraging the GoT, we design a sampler-decision maker pair that works collaboratively to achieve a shared goal. This sampling-decision making co-design is challenging since the sampler and the decision maker are strongly coupled. To decouple these processes, we formulate the problem as an infinite-horizon Decentralized Partially Observable Markov Decision Process (Dec-POMDP) to conjointly deduce the optimal joint policy. We tested the sampler-decision maker co-design in terms of goal achievement utility and sampling rate, achieving significant performance advancements over conventional state-of-the-art sampling methodologies.