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We consider a task-effective quantization problem that arises when multipleagents are controlled via a centralized controller (CC). While agents have tocommunicate their observations to the CC for decision-making, the bit-budgetedcommunications of agent-CC links may limit the task-effectiveness of the systemwhich is measured by the system's average sum of stage costs/rewards. As aresult, each agent should compress/quantize its observation such that theaverage sum of stage costs/rewards of the control task is minimally impacted.We address the problem of maximizing the average sum of stage rewards byproposing two different Action-Based State Aggregation (ABSA) algorithms thatcarry out the indirect and joint design of control and communication policiesin the multi-agent system. While the applicability of ABSA-1 is limited tosingle-agent systems, it provides an analytical framework that acts as astepping stone to the design of ABSA-2. ABSA-2 carries out the joint design ofcontrol and communication for a multi-agent system. We evaluate the algorithms- with average return as the performance metric - using numerical experimentsperformed to solve a multi-agent geometric consensus problem. The numericalresults are concluded by introducing a new metric that measures theeffectiveness of communications in a multi-agent system.

Task-Effective Compression of Observations for the Centralized Control of a Multi-agent System Over Bit-Budgeted Channels