Safe Reinforcement Learning Under High Relative Degree Constraints for Discrete‐Time Fully Cooperative Games

ABSTRACT This article investigates fully cooperative (FC) games of discrete‐time systems under high relative degree constraints and employs a reinforcement learning algorithm framework. In FC games, all players collaborate to achieve a shared objective. Addressing safety issues, previous algorithms have predominantly focused on optimal solutions under first‐order constraints. Our algorithm innovatively combines the n‐step value iteration algorithm with multi‐player high‐order discrete‐time exponential control barrier functions, ensuring both the safety and optimality of the algorithm. Additionally, we utilize neural networks within an actor‐critic framework to approximate the control policies and value functions, respectively. Experiments are carried out to validate the proposed algorithm's safety and efficiency.