Persistent monitoring of dynamic targets is essential in real-world applications such as disaster response, environmental sensing, and wildlife conservation, where mobile agents must continuously gather information under uncertainty. We propose COMPASS, a multi-agent reinforcement learning (MARL) framework that enables decentralized agents to persistently monitor multiple moving targets efficiently. We model the environment as a graph, where nodes represent spatial locations and edges capture topological proximity, allowing agents to reason over structured layouts and revisit informative regions as needed. Each agent independently selects actions based on a shared spatio-temporal attention network that we design to integrate historical observations and spatial context. We model target dynamics using Gaussian Processes (GPs), which support principled belief updates and enable uncertainty-aware planning. We train COMPASS using centralized value estimation and decentralized policy execution under an adaptive reward setting. Our extensive experiments demonstrate that COMPASS consistently outperforms strong baselines in uncertainty reduction, target coverage, and coordination efficiency across dynamic multi-target scenarios.
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