Network of Bandits insure Privacy of end-users

In order to distribute the best 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 the players are drawn from a distribution. This architecture guarantees privacy to end users since no data are stored. The only thing that can be observed through the core network is aggregated information across users. We provide a first algorithm, Distributed Median Elimination, which can be used to distribute the best arm identification task on the Mobile Edge Computing application servers. In comparison to Median Elimination run on a single player, we showed a near optimal speed-up factor in $O(N/2 K \ln^2 K)$, where $K$ is the number of actions, $N$ is the number of players. This speed-up factor is reached with a near optimal communication cost, which does not depend on the time horizon. Experiments illustrate and complete the analysis. In comparison to Median Elimination performed on each player, according to the analysis Distributed Median Elimination shows significant practical improvements.