We study the problem of synchronizing two players in a \emph{distributed multi-armed bandit} setting. The probability of \emph{synchronization error} is analyzed by recasting synchronization as a \emph{communication problem}. Using a well-designed random coding ensemble, we derive error exponents for the maximum-likelihood decoder. We then introduce a \emph{universal decoder} that achieves the same error exponents as the optimal decoder. Finally, applying these results to distributed multi-armed bandits, we show an upper bound on the regret of our synchronization scheme.

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