Multiarmed Bandits With Limited Expert Advice

We solve the COLT 2013 open problem of citetSCB on minimizing regret in the setting of advice-efficient multiarmed bandits with expert advice. We give an algorithm for the setting of K arms and N experts out of which we are allowed to query and use only M experts' advices in each round, which has a regret bound of tildeObigP√fracminK, M NM T after T rounds. We also prove that any algorithm for this problem must have expected regret at least tildeOmegabigP√fracminK, M NMT, thus showing that our upper bound is nearly tight.