To improve the performance of multi-agent reinforcement learning under the constraint of wireless resources, we propose a message importance metric and design an importance-aware scheduling policy to effectively exchange messages. The key insight is spending the precious communication resources on important messages. The message importance depends not only on the messages themselves, but also on the needs of agents who receive them. Accordingly, we propose a query-message-based architecture, called QMNet. Agents generate queries and messages with the environment observation. Sharing queries can help calculate message importance. Exchanging messages can help agents cooperate better. Besides, we exploit the message importance to deal with random access collisions in decentralized systems. Furthermore, a message prediction mechanism is proposed to compensate for messages that are not transmitted. Finally, we evaluate the proposed schemes in a traffic junction environment, where only a fraction of agents can send messages due to limited wireless resources. Results show that QMNet can extract valuable information to guarantee the system performance even when only $30\%$ of agents can share messages. By exploiting message prediction, the system can further save $40\%$ of wireless resources. The importance-aware decentralized multi-access mechanism can effectively avoid collisions, achieving almost the same performance as centralized scheduling.

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