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In this paper, we explore optimization-based and data-driven solutions in a reconfigurable intelligent surface (RIS)-aided multi-user mobile edge computing (MEC) system, where the user equipment (UEs) can partially offload their computation tasks to the access point (AP). We aim at maximizing the total completed task-input bits (TCTB) of all UEs with limited energy budgets during a given time slot, through jointly optimizing the RIS reflecting coefficients, the AP's receive beamforming vectors, and the UEs' energy partition strategies for local computing and offloading. A three-step block coordinate descending (BCD) algorithm is first proposed to effectively solve the non-convex TCTB maximization problem with guaranteed convergence. In order to reduce the computational complexity and facilitate lightweight online implementation of the optimization algorithm, we further construct two deep learning architectures …