A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization

2012/03/30 by Ali Jalali, Javad Azimi, Jalali, Ali +6
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1204.0047

ECML 2013

openalex publication_date 2012/03/30 · arxiv created 2013/07/16 · arxiv updated 2013/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. 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. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.

Citations

• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Lipschitzian optimization without the Lipschitz constant

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