Recently, Mobile-Edge Computing (MEC) has been considered as a powerful supplement to a wireless network by processing computationally intensive tasks for resource-limited mobile devices. However, despite saving computational energy at User Equipment (UE), there is additional transmission energy consumption. As a result, the joint offloading strategy should be carefully selected to save energy and computational time. In this work, we investigated a sum cost minimization problem in a multi-UE multi-computing access point (CAP) system with time-varying channels. Our approach combines the optimization-based resource allocation algorithm with a Q-learning-based strategy selection mechanism. Without the need for communication overhead for CSI and inter- neighborhood cost value exchange, our algorithm shows prominent performance over the benchmark schemes with moderate assumptions.