Cooperative multi-agent reinforcement learning with entangled state representations and copula-based action coordination for urban navigation

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Cooperative multi-agent reinforcement learning (MARL) enables autonomous agents to coordinate in complex spatial environments. This study proposes a MARL framework for goal-directed navigation that integrates entangled state embeddings, copula-based joint action transformations, and a shared reward mechanism. Entangled representations enhance cooperative awareness by incorporating peer-agent information, while copula transformations model dependence among actions to stabilize joint decision-making. A shared reward structure further aligns agent objectives toward collective performance. The framework is evaluated in synthetic continuous navigation environments and a Chicago crime-based real-data setting. Simulation studies compare three configurations: a full Copula Model, a No Copula model, and a Baseline model without cooperative enhancements. Results show that the Copula Model achieves the highest cumulative reward and the most stable coordination, whereas the Baseline model consistently underperforms. Sensitivity analysis indicates that intermediate actor learning rates provide the most stable convergence. Trajectory analyses reveal emergent cooperative behaviors such as spatial dispersion, obstacle avoidance, and coordinated movement toward target regions. In the Chicago crime experiment, agents exhibit risk-aware navigation and non-redundant exploration despite environmental complexity and sparse rewards. Overall, the findings demonstrate that combining relational state representations, copula-based dependence modeling, and shared rewards improves coordination, robustness, and stability in multi-agent navigation tasks.