# PI is back! Switching Acquisition Functions in Bayesian Optimization

arXiv: https://arxiv.org/abs/2211.01455 · HTML: https://mlsanity.com/paper/2211.01455/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Meta-Learning Acquisition Functions for Transfer Learning in Bayesian Optimization](https://mlsanity.com/paper/1904.02642/) (2019)
- [Tuning Hyperparameters without Grad Students: Scalable and Robust Bayesian Optimisation with Dragonfly](https://mlsanity.com/paper/1903.06694/) (2019)
- [Improving the Expected Improvement Algorithm](https://mlsanity.com/paper/1705.10033/) (2017)
- [Automated Dynamic Algorithm Configuration](https://mlsanity.com/paper/2205.13881/) (2022)
- [Learning Heuristic Selection with Dynamic Algorithm Configuration](https://mlsanity.com/paper/2006.08246/) (2020)
- [Towards Assessing the Impact of Bayesian Optimization's Own Hyperparameters](https://mlsanity.com/paper/1908.06674/) (2019)
- [Initial Design Strategies and their Effects on Sequential Model-Based Optimization](https://mlsanity.com/paper/2003.13826/) (2020)

## Built on by (most cited first, 6 of 6)

- [Exploring Exploration in Bayesian Optimization](https://mlsanity.com/paper/2502.08208/) (2025)
- [Self-Adjusting Weighted Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2306.04262/) (2023)
- [Mastering the exploration-exploitation trade-off in Bayesian Optimization](https://mlsanity.com/paper/2305.08624/) (2023)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)
- [Efficient Deep Learning Board: Training Feedback Is Not All You Need](https://mlsanity.com/paper/2410.14743/) (2024)
- [A Critical Examination of Active Learning Workflows in Materials Science](https://mlsanity.com/paper/2601.05946/) (2026)

## Abstract (arXiv)

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.