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In this paper, we propose a novel distributed resource allocation mechanism for semi-grant-free non-orthogonal multiple access (SGF-NOMA) transmission to maximize the network throughput, where multi-agent deep reinforcement learning with prioritized experience replay (PER) is employed. We design a centralized training framework and decentralized decision making to increase the flexibility of the proposed scheme. More specifically, each grant-free user as an "agent" learns the dynamics of the environment and makes its decisions independently in a decentralized manner. No heavy information exchange is needed to find the optimal transmit power and sub-channel that maximize the throughput. Numerical results show that the proposed algorithm with PER enhances the learning efficiency compared to the algorithm with conventional replay buffer and outperforms the existing scheme with a 12% throughput …