  Bayesian Optimization (BO) is a class of surrogate-based, sample-efficient
algorithms for optimizing black-box problems with small evaluation budgets. The
BO pipeline itself is highly configurable with many different design choices
regarding the initial design, surrogate model, and acquisition function (AF).
Unfortunately, our understanding of how to select suitable components for a
problem at hand is very limited. In this work, we focus on the definition of
the AF, whose main purpose is to balance the trade-off between exploring
regions with high uncertainty and those with high promise for good solutions.
We propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let
the exploration-exploitation trade-off self-adjust in a data-driven manner,
based on a convergence criterion for BO. On the noise-free black-box BBOB
functions of the COCO benchmarking platform, our method exhibits a favorable
any-time performance compared to handcrafted baselines and serves as a robust
default choice for any problem structure. The suitability of our method also
transfers to HPOBench. With SAWEI, we are a step closer to on-the-fly,
data-driven, and robust BO designs that automatically adjust their sampling
behavior to the problem at hand.
