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Bayesian Optimization (BO) is a powerful, sample-efficient technique tooptimize expensive-to-evaluate functions. Each of the BO components, such asthe surrogate model, the acquisition function (AF), or the initial design, issubject to a wide range of design choices. Selecting the right components for agiven optimization task is a challenging task, which can have significantimpact on the quality of the obtained results. In this work, we initiate theanalysis of which AF to favor for which optimization scenarios. To this end, webenchmark 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. Oneschedule 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 alsocompare this to a random schedule and round-robin selection of EI and PI. Weobserve that dynamic schedules oftentimes outperform any single static one. Ourresults suggest that a schedule that allocates the first 25 % of theoptimization budget to EI and the last 75 % to PI is a reliable default.However, we also observe considerable performance differences for the 24functions, suggesting that a per-instance allocation, possibly learned on thefly, could offer significant improvement over the state-of-the-art BO designs.

PI is back! Switching Acquisition Functions in Bayesian Optimization