Multi-agent reinforcement learning provides promising prospect for task scheduling in cloud-edge computing environment in recent years. However, there remains a formidable challenge due to partial observation and the rigid coupling between action spaces and schedulable devices. These limit the ability of agent to perceive global communication patterns and adapt to dynamic environments, resulting in unsatisfactory scheduling decisions. To address these issues, this work proposes SPAD, a novel spatial perception and action decoupling empowered distributed multi-agent AI task scheduling framework. By constructing a global spatial feature distillation mechanism, SPAD can approximate the implicit heterogeneous connection patterns and communication dynamics between devices and tasks under constrained observability, enhancing its ability to make robust decisions in dynamic environments with limited observations. Additionally, SPAD employs a Lyapunov-based action decoupling module to alleviate scalability challenges from rigid action-device coupling, while a novel intrinsic penalty mechanism augments the agent’s advantage function with the instantaneous Lyapunov cost, thereby aligning the policy optimization process with the decoupling module’s underlying stability constraints. Through a comprehensive empirical evaluation spanning synthetic, bursty, and real-world trace-driven workloads, we show that SPAD consistently outperforms state-of-the-art benchmarks in reducing task completion latency and improving resource utilization, while maintaining remarkable resilience and scalability across diverse network topologies and under non-stationary load conditions.