Content caching in small base stations or wireless infostations is considered to be a suitable approach to improve the efficiency in wireless content delivery. Placing the optimal content into local caches is crucial due to storage limitations, but it requires knowledge about the content popularity distribution, which is often not available in advance. Moreover, local content popularity is subject to fluctuations since mobile users with different interests connect to the caching entity over time. Which content a user prefers may depend on the user's context. In this paper, we propose a novel algorithm for context-aware proactive caching. The algorithm learns context-specific content popularity online by regularly observing context information of connected users, updating the cache content and observing cache hits subsequently. We derive a sublinear regret bound, which characterizes the learning speed and proves that our algorithm converges to the optimal cache content placement strategy in terms of maximizing the number of cache hits. Furthermore, our algorithm supports service differentiation by allowing operators of caching entities to prioritize customer groups. Our numerical results confirm that our algorithm outperforms state-of-the-art algorithms in a real world data set, with an increase in the number of cache hits of at least 14%.