An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimization

• URL: http://arxiv.org/abs/2403.05425v1
• Date: Fri, 8 Mar 2024 16:21:08 GMT
• Title: An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimization
• Authors: Shouri Hu, Jiawei Li, and Zhibo Cai
• Abstract summary: We propose a two-step optimization framework to extend BO to high-dimensional settings. Our algorithm offers the flexibility to operate these steps either concurrently or in sequence. Numerical experiments validate the efficacy of our method in challenging scenarios.
• Score: 6.79843988450982
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this challenge by proposing a two-step optimization framework. Initially, we identify the effective dimension reduction (EDR) subspace for the objective function using the minimum average variance estimation (MAVE) method. Subsequently, we construct a Gaussian process model within this EDR subspace and optimize it using the expected improvement criterion. Our algorithm offers the flexibility to operate these steps either concurrently or in sequence. In the sequential approach, we meticulously balance the exploration-exploitation trade-off by distributing the sampling budget between subspace estimation and function optimization, and the convergence rate of our algorithm in high-dimensional contexts has been established. Numerical experiments validate the efficacy of our method in challenging scenarios.

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