  In this paper, the edge caching problem in fog radio access network (F-RAN)
is investigated. By maximizing the overall cache hit rate, the edge caching
optimization problem is formulated to find the optimal policy. Content
popularity in terms of time and space is considered from the perspective of
regional users. We propose an online content popularity prediction algorithm by
leveraging the content features and user preferences, and an offline user
preference learning algorithm by using the {online gradient descent} (OGD)
method and the {follow the (proximally) regularized leader} (FTRL-Proximal)
method. Our proposed edge caching policy not only can promptly predict the
future content popularity in an online fashion with low complexity, {but also}
can track the content popularity with spatial and temporal popularity dynamic
in time without delay. Furthermore, we design two learning based edge caching
architectures. Moreover, we theoretically derive the upper bound of the
popularity prediction error, the lower bound of the cache hit rate, and the
regret bound of the overall cache hit rate of our proposed edge caching policy.
Simulation results show that the overall cache hit rate of our proposed policy
is superior to those of the traditional policies and asymptotically approaches
the optimal performance.
