A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization

Ali Jalali, Javad Azimi, Xiaoli Z. Fern, Ruofei Zhang

ECML-PKDD 2013 pp. 210-224

doi:10.1007/978-3-642-40988-2_14 /ecmlpkdd/2013/jalali2013ecmlpkdd-lipschitz/

Abstract

The problem of optimizing unknown costly-to-evaluate functions has been studied extensively in the context of Bayesian optimization. Algorithms in this field aim to find the optimizer of the function by requesting only a few function evaluations at carefully selected locations. An ideal algorithm should maintain a perfect balance between exploration (probing unexplored areas) and exploitation (focusing on promising areas) within the given evaluation budget. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible, while the exploitation phase focuses on the reduced search space and selects samples closest to the optimizer. We empirically show that the proposed algorithm significantly outperforms the baseline algorithms.

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Cite

Text

Jalali et al. "A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2013. doi:10.1007/978-3-642-40988-2_14

Markdown

[Jalali et al. "A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2013.](https://mlanthology.org/ecmlpkdd/2013/jalali2013ecmlpkdd-lipschitz/) doi:10.1007/978-3-642-40988-2_14

BibTeX

@inproceedings{jalali2013ecmlpkdd-lipschitz,
  title     = {{A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization}},
  author    = {Jalali, Ali and Azimi, Javad and Fern, Xiaoli Z. and Zhang, Ruofei},
  booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
  year      = {2013},
  pages     = {210-224},
  doi       = {10.1007/978-3-642-40988-2_14},
  url       = {https://mlanthology.org/ecmlpkdd/2013/jalali2013ecmlpkdd-lipschitz/}
}