  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.
