Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization
Machine Learning
2022-07-06 v4 Optimization and Control
Machine Learning
Abstract
We consider the problem of maximizing a non-concave Lipschitz multivariate function over a compact domain by sequentially querying its (possibly perturbed) values. We study a natural algorithm designed originally by Piyavskii and Shubert in 1972, for which we prove new bounds on the number of evaluations of the function needed to reach or certify a given optimization accuracy. Our analysis uses a bandit-optimization viewpoint and solves an open problem from Hansen et al.\ (1991) by bounding the number of evaluations to certify a given accuracy with a near-optimal sum of packing numbers.
Cite
@article{arxiv.2002.02390,
title = {Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization},
author = {Clément Bouttier and Tommaso Cesari and Mélanie Ducoffe and Sébastien Gerchinovitz},
journal= {arXiv preprint arXiv:2002.02390},
year = {2022}
}