  Communication is one of the core components for cooperative multi-agent
reinforcement learning (MARL). The communication bandwidth, in many real
applications, is always subject to certain constraints. To improve
communication efficiency, in this article, we propose to simultaneously
optimize whom to communicate with and what to communicate for each agent in
MARL. By initiating the communication between agents with a directed complete
graph, we propose a novel communication model, named Communicative Graph
Information Bottleneck Network (CGIBNet), to simultaneously compress the graph
structure and the node information with the graph information bottleneck
principle. The graph structure compression is designed to cut the redundant
edges for determining whom to communicate with. The node information
compression aims to address the problem of what to communicate via learning
compact node representations. Moreover, CGIBNet is the first universal module
for bandwidth-constrained communication, which can be applied to various
training frameworks (i.e., policy-based and value-based MARL frameworks) and
communication modes (i.e., single-round and multi-round communication).
Extensive experiments are conducted in Traffic Control and StarCraft II
environments. The results indicate that our method can achieve better
performance in bandwidth-constrained settings compared with state-of-the-art
algorithms.
