Two algorithms for bandits with Erdős-Rényi side observations achieve regret O(sqrt((T/r) log N)) when r is not too small and O(sqrt((T/r) log (N+T))) otherwise, within log factors of the optimum even if r were known.
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Online learning with Erd\H{o}s-R\'enyi side-observation graphs
Two algorithms for bandits with Erdős-Rényi side observations achieve regret O(sqrt((T/r) log N)) when r is not too small and O(sqrt((T/r) log (N+T))) otherwise, within log factors of the optimum even if r were known.