Amid the escalating complexity of networks, wireless intelligent devices, constrained by energy and resources, bear the increasing burden of managing various tasks. The decision of whether to allocate tasks to edge servers or handle them locally on devices now significantly impacts network performance. This study focuses on optimizing task-offloading decisions to balance network latency and energy consumption. An advanced learning-based multi-objective bat algorithm, MOBA-CV-SARSA, tailored to the constraints of wireless devices, presents a promising solution for edge computing task offloading. Developed in C++, MOBA-CV-SARSA demonstrates significant improvements over NSGA-RL-CV and QLPSO-CV, enhancing hypervolume and diversity-metric indicators by 0.9%, 15.07%, 4.72%, and 0.1%, respectively. Remarkably, MOBA-CV-SARSA effectively reduces network energy consumption within acceptable latency thresholds. Moreover, integrating an automatic switching mechanism enables MOBA-CV-SARSA to accelerate convergence speed while conserving 150.825 W of energy, resulting in a substantial 20.24% reduction in overall network energy consumption.