High Dimensional Bayesian Optimization Assisted by Principal Component Analysis

TL;DR

This paper introduces PCA-assisted Bayesian Optimization (PCA-BO), which combines principal component analysis with Gaussian Process-based BO to improve scalability and efficiency in high-dimensional optimization problems.

Contribution

The paper proposes a novel PCA-BO algorithm that learns a linear transformation to reduce dimensionality, enhancing computational efficiency while maintaining convergence.

Findings

PCA-BO reduces CPU time on high-dimensional problems.

PCA-BO maintains convergence rate with adequate global structure.

Effective trade-off between convergence and efficiency achieved.

Abstract

Bayesian Optimization (BO) is a surrogate-assisted global optimization technique that has been successfully applied in various fields, e.g., automated machine learning and design optimization. Built upon a so-called infill-criterion and Gaussian Process regression (GPR), the BO technique suffers from a substantial computational complexity and hampered convergence rate as the dimension of the search spaces increases. Scaling up BO for high-dimensional optimization problems remains a challenging task. In this paper, we propose to tackle the scalability of BO by hybridizing it with a Principal Component Analysis (PCA), resulting in a novel PCA-assisted BO (PCA-BO) algorithm. Specifically, the PCA procedure learns a linear transformation from all the evaluated points during the run and selects dimensions in the transformed space according to the variability of evaluated points. We then construct the GPR model, and the infill-criterion in the space spanned by the selected dimensions. We assess the performance of our PCA-BO in terms of the empirical convergence rate and CPU time on multi-modal problems from the COCO benchmark framework. The experimental results show that PCA-BO can effectively reduce the CPU time incurred on high-dimensional problems, and maintains the convergence rate on problems with an adequate global structure. PCA-BO therefore provides a satisfactory trade-off between the convergence rate and computational efficiency opening new ways to benefit from the strength of BO approaches in high dimensional numerical optimization.