Centralized Control of a Multi-Agent System Via Distributed and Bit-Budgeted Communications

We consider a distributed quantization problem that arises when multiple edge devices, i.e., agents, are controlled via a centralized controller (CC). While agents have to communicate their observations to the CC for decision-making, the bit-budgeted communications of agent-CC links may limit the task-effectiveness of the system which is measured by the system's average sum of stage costs/rewards. As a result, each agent, given its local processing resources, should compress/quantize its observation such that the average sum of stage costs/rewards of the control task is minimally impacted. We address the problem of maximizing the average sum of stage rewards by proposing two different Action-Based State Aggregation (ABSA) algorithms that carry out the indirect and joint design of control and communication policies in the multi-agent system (MAS). While the applicability of ABSA-1 is limited to single-agent systems, it provides an analytical framework that acts as a stepping stone to the design of ABSA-2. ABSA-2 carries out the joint design of control and communication for an MAS. We evaluate the algorithms - with average return as the performance metric - using numerical experiments performed to solve a multi-agent geometric consensus problem.