In multi-access edge computing (MEC), mobile users (MUs) can offload computation tasks to nearby computational resources, which are owned by a mobile network operator (MNO), to save energy. In this work, we investigate two important challenges of task offloading in MEC: (i) The techno-economic interactions of the MNO and the MUs. The MNO faces a profit maximization problem, whereas the MUs face an energy minimization problem. (ii) Limited information at the MUs about the MNO's communication and computation resources and the task offloading strategies of other MUs. To overcome these challenges, we model the task offloading problem as a matching game between the MUs and the MNO including their techno-economic interactions. Furthermore, we propose a novel Collision-Avoidance Task Offloading Multi-Armed-Bandit (CA-TO-MAB) algorithm, that allows the MUs to learn the amount of available resources at the MNO and the task offloading strategies of other MUs in an online, fully decentralized way. We show that by using CA-TO-MAB, the cumulative revenue of the MNO can be increased by 25% and, at the same time the energy consumption of the MUs can be reduced by 6% compared to state-of-the-art online learning algorithms for task offloading. Furthermore, the communication overhead can be reduced by 55% compared to a non-learning game-theoretic approach.