Digital immersion via Virtual Reality (VR) and Augmented Reality (AR) applications is expected to be a key driver of growth for the 5G mobile network. The immersive requirement imposes many technical challenges. On one hand, Mobile Edge Computing (MEC) is an effective network paradigm to provide low transmission latency and massive computation for 360° videos. On the other hand, viewport adaptive streaming also provides a bandwidth efficient solution. Accordingly, in this paper, we investigate the caching policy for tile-based 360° videos in an MEC caching system. Our goal is to find the optimal caching policy to co-optimize users’ quality of experience (QoE) and MEC energy consumption with no a-priori knowledge on video content popularity. We apply the combinatorial multi-armed bandit (CMAB) theory to solve the above problem which is a sequential decision making problem. On the basis of the combinatorial UCB (CUCB), an improved algorithm is proposed to speed up learning process. The outcome of the algorithm is the caching decision for each time slot. The effectiveness of the proposed learning based caching policy is confirmed by simulation results in terms of the learning speed, hit rate, energy consumption and request latency.