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Lai and Robbins (1985) and Lai (1987) provided efficient parametric solutionsto the multi-armed bandit problem, showing that arm allocation via upperconfidence bounds (UCB) achieves minimum regret. These bounds are constructedfrom the Kullback-Leibler information of the reward distributions, estimatedfrom specified parametric families. In recent years there has been renewedinterest in the multi-armed bandit problem due to new applications in machinelearning algorithms and data analytics. Non-parametric arm allocationprocedures like $\epsilon$-greedy, Boltzmann exploration and BESA were studied,and modified versions of the UCB procedure were also analyzed undernon-parametric settings. However unlike UCB these non-parametric procedures arenot efficient under general parametric settings. In this paper we proposeefficient non-parametric procedures.

The Multi-Armed Bandit Problem: An Efficient Non-Parametric Solution