Efficient resource utilization is proposed for simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) to ensure fair and high data rates. We optimize the number of STAR-RIS elements to be allocated to each user and maximize the sum of the user rates. To promote fairness, we introduce a soft fairness mechanism that guarantees a minimum STAR-RIS element allocation to every user. Subject to this requirement, the phase shifts of the STAR-RIS elements and the remaining element assignments are jointly optimized by harnessing an appropriately tailored deep reinforcement learning (DRL) algorithm. The proposed DRL method is also compared to Dinkelbach's algorithm and to a bespoke hybrid DRL approach. A deactivation incentive is incorporated into the DRL model for enhancing resource utilization by intelligently deactivating some of the STAR-RIS elements when not required. The proposed DRL method achieves fair and high data rates for both stationary and mobile users, while ensuring efficient resource utilization. Using the proposed DRL method, up to 34% and 23% of STAR-RIS elements can be deactivated in static and mobile scenarios, respectively, with negligible degradation in the average DL data rate.

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