Adaptive traffic signal control (ATSC) is crucial in reducing congestion, maximizing throughput, and improving mobility in rapidly growing urban areas. Recent advancements in parameter-sharing multi-agent reinforcement learning (MARL) have greatly enhanced the scalable and adaptive optimization of complex, dynamic flows in large-scale homogeneous networks. However, the inherent heterogeneity of real-world traffic networks, with their varied intersection topologies and interaction dynamics, poses substantial challenges to achieving scalable and effective ATSC across different traffic scenarios. To address these challenges, we present Unicorn, a universal and collaborative MARL framework designed for efficient and adaptable network-wide ATSC. Specifically, we first propose a unified approach to map the states and actions of intersections with varying topologies into a common structure based on traffic movements. Next, we design a Universal Traffic Representation (UTR) module with a decoder-only network for general feature extraction, enhancing the model's adaptability to diverse traffic scenarios. Additionally, we incorporate an Intersection Specifics Representation (ISR) module, designed to identify key latent vectors that represent the unique intersection's topology and traffic dynamics through variational inference techniques. To further refine these latent representations, we employ a contrastive learning approach in a self-supervised manner, which enables better differentiation of intersection-specific features. Moreover, we integrate the state-action dependencies of neighboring agents into policy optimization, which effectively captures dynamic agent interactions and facilitates efficient regional collaboration. [...]. The code is available at https://github.com/marmotlab/Unicorn

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