  With countless promising applications in various domains such as IoT and
industry 4.0, task-oriented communication design (TOCD) is getting accelerated
attention from the research community. This paper presents a novel approach for
designing scalable task-oriented quantization and communications in cooperative
multi-agent systems (MAS). The proposed approach utilizes the TOCD framework
and the value of information (VoI) concept to enable efficient communication of
quantized observations among agents while maximizing the average return
performance of the MAS, a parameter that quantifies the MAS's task
effectiveness. The computational complexity of learning the VoI, however, grows
exponentially with the number of agents. Thus, we propose a three-step
framework: i) learning the VoI (using reinforcement learning (RL)) for a
two-agent system, ii) designing the quantization policy for an $N$-agent MAS
using the learned VoI for a range of bit-budgets and, (iii) learning the
agents' control policies using RL while following the designed quantization
policies in the earlier step. We observe that one can reduce the computational
cost of obtaining the value of information by exploiting insights gained from
studying a similar two-agent system - instead of the original $N$-agent system.
We then quantize agents' observations such that their more valuable
observations are communicated more precisely. Our analytical results show the
applicability of the proposed framework under a wide range of problems.
Numerical results show striking improvements in reducing the computational
complexity of obtaining VoI needed for the TOCD in a MAS problem without
compromising the average return performance of the MAS.
