Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings
This addresses the challenge of efficient exploration in high-dimensional Bayesian optimization for researchers and practitioners, offering a novel approach that is incremental over existing methods.
The paper tackles the problem of high-dimensional black-box function optimization by proposing a method that operates directly in the high-dimensional space using learned low-dimensional structure, avoiding biased reconstruction issues. It demonstrates effectiveness on benchmarks and a real-world function, handling thousands of dimensions without computational difficulty.
The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into optimization in a low-dimensional space. They exploit the low-dimensional structure and reduce the computational burden. However, we reveal that this approach could be limited or inefficient in exploring the high-dimensional space mainly due to the biased reconstruction of the high-dimensional queries from the low-dimensional queries. In this paper, we investigate a simple alternative approach: tackling the problem in the original high-dimensional space using the information from the learned low-dimensional structure. We provide a theoretical analysis of the exploration ability. Furthermore, we show that our method is applicable to batch optimization problems with thousands of dimensions without any computational difficulty. We demonstrate the effectiveness of our method on high-dimensional benchmarks and a real-world function.