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This article presents a supervised multi-agent safe policy learning (SMAS-PL) method for optimal power management of networked microgrids (MGs) in distribution systems. While unconstrained reinforcement learning (RL) algorithms are black-box decision models that could fail to satisfy grid operational constraints, our proposed method considers AC power flow equations and other operational limits. Accordingly, the training process employs the gradient information of operational constraints to ensure that the optimal control policy functions generate safe and feasible decisions. Furthermore, we have developed a distributed consensus-based optimization approach to train the agents' policy functions while maintaining MGs' privacy and data ownership boundaries. After training, the learned optimal policy functions can be safely used by the MGs to dispatch their local resources, without the need to solve a complex …