In this paper, we consider the downlink transmission of a multi-antenna base station (BS) supported by an active simultaneously transmitting and reconfigurable intelligent surface (STAR-RIS) to serve single-antenna users via simultaneous wireless information and power transfer (SWIPT). In this context, we formulate an energy efficiency maximisation problem that jointly optimises the gain, element selection and phase shift matrices of the active STAR-RIS, the transmit beamforming of the BS and the power splitting ratio of the users. With respect to the highly coupled and non-convex form of this problem, an alternating optimisation solution approach is proposed, using tools from convex optimisation and reinforcement learning. Specifically, semi-definite relaxation (SDR), difference of concave functions (DC), and fractional programming techniques are employed to transform the non-convex optimisation problem into a convex form for optimising the BS beamforming vector and the power splitting ratio of the SWIPT. Then, by integrating meta-learning with the modified deep deterministic policy gradient (DDPG) and soft actor-critical (SAC) methods, a combinatorial reinforcement learning network is developed to optimise the element selection, gain and phase shift matrices of the active STAR-RIS. Our simulations show the effectiveness of the proposed resource allocation scheme. Furthermore, our proposed active STAR-RISbased SWIPT system outperforms its passive counterpart by 57% on average. Index Terms-Active simultaneously transmitting and reflecting intelligent surface (STAR-RIS), simultaneously wireless information and power transfer (SWIPT), energy efficiency (EE), convex optimisation, meta-learning, deep deterministic policy gradient (DDPG), soft actor-critic (SAC).

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