Mobile edge computing usually uses cache to support multimedia contents in 5G mobile Internet to reduce the computing overhead and latency. Mobile edge caching (MEC) systems are vulnerable to various attacks such as denial of service attacks and rogue edge attacks. This article investigates the attack models in MEC systems, focusing on both the mobile offloading and the caching procedures. In this paper, we propose security solutions that apply reinforcement learning (RL) techniques to provide secure offloading to the edge nodes against jamming attacks. We also present light-weight authentication and secure collaborative caching schemes to protect data privacy. We evaluate the performance of the RL-based security solution for mobile edge caching and discuss the challenges that need to be addressed in the future.