A novel simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) aided downlink non-orthogonal multiple access (NOMA) communication framework is proposed. Two STAR-RIS protocols are investigated, namely the energy splitting (ES) and the mode switching (MS). However, since the STAR-RIS has a massive number of reconfigurable elements, the passive beamforming problem has enormous action dimensions and extremely high complexity, resulting in an increased training time and performance degradation for the artificial intelligent agent. To resolve this predicament, a partitioning approach is proposed to divide the STAR-RIS into several tiles. A deep reinforcement learning (DRL) approach is conceived for the partitioning and the corresponding tile-based passive beamforming of the STAR-RIS, as well as the power allocation for users to maximize the average throughput. Simulation results indicate that the tile-based passive beamforming approach outperforms benchmarks while the STAR-RIS has a large size, and the ES protocol is preferred for being employed in the NOMA networks compared with the MS protocol.

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