Stochastic simultaneous optimistic optimization
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.
Cite
@article{arxiv.2604.24537,
title = {Stochastic simultaneous optimistic optimization},
author = {Michal Valko and Alexandra Carpentier and Rémi Munos},
journal= {arXiv preprint arXiv:2604.24537},
year = {2026}
}
Comments
Published in International Conference on Machine Learning (ICML 2013)