Scalable Quantification of the Value of Information for Multi-Agent Communications and Control Co-design

Task-oriented communication design (TOCD) has gained significant attention from the research community due to its numerous promising applications in domains such as
$\text{IoT}$
and industry 4.0. This paper introduces an innovative approach to designing scalable task-oriented quantization and communications in cooperative multi-agent systems (MAS). Our proposed approach leverages the TOCD framework and the concept of the value of information
$(\text{VoI})$
to facilitate efficient communication of quantized observations among agents while maximizing the average return performance of the MAS-a metric that measures the task effectiveness of the MAS. Learning the VoI becomes a prohibitively large computational problem as the number of agents grows in the MAS. To address this challenge, we present a three-step framework. First, we employ reinforcement learning (RL) to learn the VoI for a two-agent, rather than for the original
$N$
-agent system, reducing the computational costs associated with obtaining the value of information. Next, we design the quantization policy for a MAS with N agents, utilizing the learned VoI across a range of bit-budgets. The resulting quantization strategy for agents' observations, ensures that more valuable observations are communicated with greater precision. Finally, we apply RL to learn the agents' control policies, while adhering to the quantization policies designed in the previous step. Our analytical results showcase the effectiveness of the proposed framework across a wide range of problems. Numerical experiments demonstrate improvements in reducing the computational complexity required for obtaining VoI by five orders of magnitude in TOCD for MAS problems while compromising less than 1% on the average return performance of the MAS.