High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy

TL;DR

This paper introduces a novel high-dimensional Bayesian Optimization method that uses Covariance Matrix Adaptation to define local search regions, improving global optimization performance on complex black-box functions.

Contribution

It proposes a new technique leveraging CMA to identify promising local regions for BO, enhancing high-dimensional optimization efficiency and integrating with existing BO algorithms.

Findings

Outperforms state-of-the-art methods on benchmark problems

Effective in high-dimensional black-box optimization

Compatible with various existing BO algorithms

Abstract

Bayesian Optimization (BO) is an effective method for finding the global optimum of expensive black-box functions. However, it is well known that applying BO to high-dimensional optimization problems is challenging. To address this issue, a promising solution is to use a local search strategy that partitions the search domain into local regions with high likelihood of containing the global optimum, and then use BO to optimize the objective function within these regions. In this paper, we propose a novel technique for defining the local regions using the Covariance Matrix Adaptation (CMA) strategy. Specifically, we use CMA to learn a search distribution that can estimate the probabilities of data points being the global optimum of the objective function. Based on this search distribution, we then define the local regions consisting of data points with high probabilities of being the global optimum. Our approach serves as a meta-algorithm as it can incorporate existing black-box BO optimizers, such as BO, TuRBO, and BAxUS, to find the global optimum of the objective function within our derived local regions. We evaluate our proposed method on various benchmark synthetic and real-world problems. The results demonstrate that our method outperforms existing state-of-the-art techniques.