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The paper proposes a novel upper confidence bound (UCB) procedure foridentifying the arm with the largest mean in a multi-armed bandit game in thefixed confidence setting using a small number of total samples. The procedurecannot be improved in the sense that the number of samples required to identifythe best arm is within a constant factor of a lower bound based on the law ofthe iterated logarithm (LIL). Inspired by the LIL, we construct our confidencebounds to explicitly account for the infinite time horizon of the algorithm. Inaddition, by using a novel stopping time for the algorithm we avoid a unionbound over the arms that has been observed in other UCB-type algorithms. Weprove that the algorithm is optimal up to constants and also show throughsimulations that it provides superior performance with respect to thestate-of-the-art.

lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits