Lipschitz Bandit Optimization with Improved Efficiency
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We consider the Lipschitz bandit optimization problem with an emphasis on practical efficiency. Although there is rich literature on regret analysis of this type of problem, e.g., [Kleinberg et al. 2008, Bubeck et al. 2011, Slivkins 2014], their proposed algorithms suffer from serious practical problems including extreme time complexity and dependence on oracle implementations. With this motivation, we propose a novel algorithm with an Upper Confidence Bound (UCB) exploration, namely Tree UCB-Hoeffding, using adaptive partitions. Our partitioning scheme is easy to implement and does not require any oracle settings. With a tree-based search strategy, the total computational cost can be improved to O(T T) for the first T iterations. In addition, our algorithm achieves the regret lower bound up to a logarithmic factor.
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