  We develop Gibbs sampling based techniques for learning the optimal content
placement in a cellular network. A collection of base stations are scattered on
the space, each having a cell (possibly overlapping with other cells). Mobile
users request for downloads from a finite set of contents according to some
popularity distribution. Each base station can store only a strict subset of
the contents at a time; if a requested content is not available at any serving
base station, it has to be downloaded from the backhaul. Thus, there arises the
problem of optimal content placement which can minimize the download rate from
the backhaul, or equivalently maximize the cache hit rate. Using similar ideas
as Gibbs sampling, we propose simple sequential content update rules that
decide whether to store a content at a base station based on the knowledge of
contents in neighbouring base stations. The update rule is shown to be
asymptotically converging to the optimal content placement for all nodes. Next,
we extend the algorithm to address the situation where content popularities and
cell topology are initially unknown, but are estimated as new requests arrive
to the base stations. Finally, improvement in cache hit rate is demonstrated
numerically.
