PI is back! Switching Acquisition Functions in Bayesian Optimization

Bayesian Optimization (BO) is a powerful, sample-efficient technique to optimize expensive-to-evaluate functions. Each of the BO components, such as the surrogate model, the acquisition function (AF), or the initial design, is subject to a wide range of design choices. Selecting the right components for a given optimization task is a challenging task, which can have significant impact on the quality of the obtained results. In this work, we initiate the analysis of which AF to favor for which optimization scenarios. To this end, we benchmark SMAC3 using Expected Improvement (EI) and Probability of Improvement (PI) as acquisition functions on the 24 BBOB functions of the COCO environment. We compare their results with those of schedules switching between AFs. One schedule aims to use EI's explorative behavior in the early optimization steps, and then switches to PI for a better exploitation in the final steps. We also compare this to a random schedule and round-robin selection of EI and PI. We observe that dynamic schedules oftentimes outperform any single static one. Our results suggest that a schedule that allocates the first 25 % of the optimization budget to EI and the last 75 % to PI is a reliable default. However, we also observe considerable performance differences for the 24 functions, suggesting that a per-instance allocation, possibly learned on the fly, could offer significant improvement over the state-of-the-art BO designs.