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**Stochastic Simultaneous Optimistic Optimization**

**Authors:** *Michal Valko*, *Alexandra Carpentier* and *Rémi Munos*

**Conference:** Proceedings of the 30th International Conference on Machine Learning (ICML-13)

**Year:** 2013

**Pages:** 19-27

**Abstract:** We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.

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