Caching with Unknown Popularity Profiles in Small Cell Networks

A heterogenous network is considered where the base stations (BSs), small base stations (SBSs) and users are distributed according to independent Poisson point processes (PPPs). We let the SBS nodes to posses high storage capacity and are assumed to form a distributed caching network. Popular data files are stored in the local cache of SBS, so that users can download the desired files from one of the SBS in the vicinity subject to availability. The offloading-loss is captured via a cost function that depends on a random caching strategy proposed in this paper. The cost function depends on the popularity profile, which is, in general, unknown. In this work, the popularity profile is estimated at the BS using the available instantaneous demands from the users in a time interval $[0,\tau]$. This is then used to find an estimate of the cost function from which the optimal random caching strategy is devised. The main results of this work are the following: First it is shown that the waiting time $\tau$ to achieve an $\epsilon>0$ difference between the achieved and optimal costs is finite, provided the user density is greater than a predefined threshold. In this case, $\tau$ is shown to scale as $N^2$, where $N$ is the support of the popularity profile. Secondly, a transfer learning-based approach is proposed to obtain an estimate of the popularity profile used to compute the empirical cost function. A condition is derived under which the proposed transfer learning-based approach performs better than the random caching strategy.