  In order to distribute the best arm identification task as close as possible
to the user's devices, on the edge of the Radio Access Network, we propose a
new problem setting, where distributed players collaborate to find the best
arm. This architecture guarantees privacy to end-users since no events are
stored. The only thing that can be observed by an adversary through the core
network is aggregated information across users. We provide a first algorithm,
Distributed Median Elimination, which is optimal in term of number of
transmitted bits and near optimal in term of speed-up factor with respect to an
optimal algorithm run independently on each player. In practice, this first
algorithm cannot handle the trade-off between the communication cost and the
speed-up factor, and requires some knowledge about the distribution of players.
Extended Distributed Median Elimination overcomes these limitations, by playing
in parallel different instances of Distributed Median Elimination and selecting
the best one. Experiments illustrate and complete the analysis. According to
the analysis, in comparison to Median Elimination performed on each player, the
proposed algorithm shows significant practical improvements.
