A Parallel algorithm for X-Armed bandits
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The target of X-armed bandit problem is to find the global maximum of an unknown stochastic function f, given a finite budget of n evaluations. Recently, X-armed bandits have been widely used in many situations. Many of these applications need to deal with large-scale data sets. To deal with these large-scale data sets, we study a distributed setting of X-armed bandits, where m players collaborate to find the maximum of the unknown function. We develop a novel anytime distributed X-armed bandit algorithm. Compared with prior work on X-armed bandits, our algorithm uses a quite different searching strategy so as to fit distributed learning scenarios. Our theoretical analysis shows that our distributed algorithm is m times faster than the classical single-player algorithm. Moreover, the number of communication rounds of our algorithm is only logarithmic in mn. The numerical results show that our method can make effective use of every players to minimize the loss. Thus, our distributed approach is attractive and useful.
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