Triangulation candidates for Bayesian optimization
This work addresses a bottleneck in Bayesian optimization for researchers and practitioners, offering an incremental improvement over existing candidate-based approaches.
The paper tackles the challenge of optimizing non-convex, multi-modal, or non-differentiable acquisition functions in Bayesian optimization by proposing 'tricands' based on Delaunay triangulation, demonstrating that they outperform numerically optimized and random candidate methods in synthetic and real simulation benchmarks.
Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suited for hybrid schemes, on benchmark synthetic and real simulation experiments.