Incorporating reinforcement learning into event-triggered communication and control policies can achieve impressive control performance and considerable communication savings. Recent approaches rely on centralized training and decentralized execution paradigm to offset the missing global information, which may not always be accessible in the real world. Meanwhile, existing methods for multi-agent systems still face scalability and classical communication problems. To address these issues, we introduce a decentralized reinforcement learning algorithm with selective parameter sharing to learn hybrid action spaces in distributed multi-agent systems. Furthermore, we propose a dynamic penalty design algorithm to balance the control and communication policies.