Revisiting Bayesian Optimization in the light of the COCO benchmark
This work provides empirical guidance for practitioners using BO in optimization tasks, though it is incremental as it refines existing methods rather than introducing new paradigms.
The study systematically evaluates Bayesian optimization (BO) design choices using the COCO benchmark, finding that specific configurations (small initial budget, quadratic trend, optimized acquisition) improve performance, making best EGO variants competitive or superior to state-of-the-art algorithms for multimodal functions in dimensions ≤5.
It is commonly believed that Bayesian optimization (BO) algorithms are highly efficient for optimizing numerically costly functions. However, BO is not often compared to widely different alternatives, and is mostly tested on narrow sets of problems (multimodal, low-dimensional functions), which makes it difficult to assess where (or if) they actually achieve state-of-the-art performance. Moreover, several aspects in the design of these algorithms vary across implementations without a clear recommendation emerging from current practices, and many of these design choices are not substantiated by authoritative test campaigns. This article reports a large investigation about the effects on the performance of (Gaussian process based) BO of common and less common design choices. The experiments are carried out with the established COCO (COmparing Continuous Optimizers) software. It is found that a small initial budget, a quadratic trend, high-quality optimization of the acquisition criterion bring consistent progress. Using the GP mean as an occasional acquisition contributes to a negligible additional improvement. Warping degrades performance. The Matérn 5/2 kernel is a good default but it may be surpassed by the exponential kernel on irregular functions. Overall, the best EGO variants are competitive or improve over state-of-the-art algorithms in dimensions less or equal to 5 for multimodal functions. The code developed for this study makes the new version (v2.1.1) of the R package DiceOptim available on CRAN. The structure of the experiments by function groups allows to define priorities for future research on Bayesian optimization.