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Stochastic Simultaneous Optimistic Optimization

Michal Valko 1 Alexandra Carpentier 1, 2 Rémi Munos 1 
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 Statistical Laboratory [Cambridge]
DPMMS - Department of Pure Mathematics and Mathematical Statistics
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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Submitted on : Thursday, May 30, 2013 - 4:13:59 PM
Last modification on : Thursday, January 20, 2022 - 4:12:31 PM
Long-term archiving on: : Tuesday, September 3, 2013 - 10:15:22 AM


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  • HAL Id : hal-00789606, version 2


Michal Valko, Alexandra Carpentier, Rémi Munos. Stochastic Simultaneous Optimistic Optimization. International Conference on Machine Learning, Jun 2013, Atlanta, United States. ⟨hal-00789606v2⟩



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