Traffic congestion in modern cities is exacerbated by the limitations of traditional fixed-time traffic signal systems, which fail to adapt to dynamic traffic patterns. Adaptive Traffic Signal Control (ATSC) algorithms have emerged as a solution by dynamically adjusting signal timing based on real-time traffic conditions. However, the main limitation of such methods is that they are not transferable to environments under real-world constraints, such as balancing efficiency, minimizing collisions, and ensuring fairness across intersections. In this paper, we view the ATSC problem as a constrained multi-agent reinforcement learning (MARL) problem and propose a novel algorithm named Multi-Agent Proximal Policy Optimization with Lagrange Cost Estimator (MAPPO-LCE) to produce effective traffic signal control policies. Our approach integrates the Lagrange multipliers method to balance rewards and constraints, with a cost estimator for stable adjustment. We also introduce three constraints on the traffic network: GreenTime, GreenSkip, and PhaseSkip, which penalize traffic policies that do not conform to real-world scenarios. Our experimental results on three real-world datasets demonstrate that MAPPO-LCE outperforms three baseline MARL algorithms by across all environments and traffic constraints (improving on MAPPO by 12.60%, IPPO by 10.29%, and QTRAN by 13.10%). Our results show that constrained MARL is a valuable tool for traffic planners to deploy scalable and efficient ATSC methods in real-world traffic networks. We provide code atthis https URL.
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