Edge caching is an effective solution to reduce delivery latency and network congestion by bringing contents close to end-users. A deep understanding of content popularity and the principles underlying the content request sequence are required to effectively utilize the cache. Most existing works design caching policies based on global content requests with very limited consideration of individual content requests which reflect personal preferences. To enable the optimal caching strategy, in this article, we propose an Active learning (AL) approach to learn the content popularities and design an accurate content request prediction model. We model the content requests from user terminals as a demand matrix and then employ AL-based query-by-committee (QBC) matrix completion to predict future missing requests. The main principle of QBC is to query the most informative missing entries of the demand matrix. Based on the prediction provided by the QBC, we propose an adaptive optimization caching framework to learn popularities as fast as possible while guaranteeing an operational cache hit ratio requirement. The proposed framework is model-free, thus does not require any statistical knowledge about the underlying traffic demands. We consider both the fixed and time-varying nature of content popularities. The effectiveness of the proposed learning caching policies over the existing methods is demonstrated in terms of root mean square error, cache hit ratio, and cache size on a simulated dataset.