Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) can expand the coverage of mobile edge computing (MEC) services by reflecting and transmitting signals simultaneously, enabling full-space coverage. The orientation of the STAR-RIS plays a crucial role in optimizing the gain of received and transmitted signals, and a rotatable STAR-RIS offers potential enhancement for MEC systems. This paper investigates a rotatable STAR-RIS-assisted MEC system, operated under three protocols, namely energy splitting, mode switching, and time switching. The goal is to minimize energy consumption for multiple moving user devices through the joint optimization of STAR-RIS configurations, orientation, computation resource allocation, transmission power, and task offloading strategies. Considering the mobility of user devices, we model the original optimization problem as a sequential decision-making process across multiple time slots. The high-dimensional, highly coupled, and nonlinear nature makes it a challenging non-convex decision-making problem for traditional optimization algorithms. Therefore, a deep reinforcement learning (DRL) approach is employed, specifically utilizing soft actor-critic algorithm to train the DRL model. Simulation results demonstrate that the proposed algorithm outperforms the benchmarks in both convergence speed and energy efficiency, while reducing energy consumption by up to 52.7\% compared to the fixed STAR-RIS scheme. Among three operating protocols, the energy splitting yields the best performance.
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