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 near optimal both in terms of number of transmitted bits in terms of number of pulls per player. This first algorithm requires the distribution of players to be known. Extended Distributed Median Elimination overcomes this limitation, 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.
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