Voronoi Candidates for Bayesian Optimization
This addresses efficiency issues in Bayesian optimization for practitioners, but it is incremental as it builds on existing space-filling candidate methods.
The paper tackles the computational overhead of optimizing acquisition functions in Bayesian optimization by proposing to use candidates on the Voronoi tessellation boundary, which significantly improves execution time without loss in accuracy on test problems.
Bayesian optimization (BO) offers an elegant approach for efficiently optimizing black-box functions. However, acquisition criteria demand their own challenging inner-optimization, which can induce significant overhead. Many practical BO methods, particularly in high dimension, eschew a formal, continuous optimization of the acquisition function and instead search discretely over a finite set of space-filling candidates. Here, we propose to use candidates which lie on the boundary of the Voronoi tessellation of the current design points, so they are equidistant to two or more of them. We discuss strategies for efficient implementation by directly sampling the Voronoi boundary without explicitly generating the tessellation, thus accommodating large designs in high dimension. On a battery of test problems optimized via Gaussian processes with expected improvement, our proposed approach significantly improves the execution time of a multi-start continuous search without a loss in accuracy.