We introduce a framework that integrates variational autoencoders (VAE) with reinforcement learning (RL) to balance system performance and resource usage in multi-agent systems by dynamically adjusting network structures over time. A key innovation of this method is its capability to handle the vast action space of the network structure. This is achieved by combining Variational Auto-Encoder and Deep Reinforcement Learning to control the latent space encoded from the network structures. The proposed method, evaluated on the modified OpenAI particle environment under various scenarios, not only demonstrates superior performance compared to baselines but also reveals interesting strategies and insights through the learned behaviors.