# On Local Optimizers of Acquisition Functions in Bayesian Optimization

arXiv: https://arxiv.org/abs/1901.08350 · HTML: https://mlsanity.com/paper/1901.08350/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2019.

## Built on by (most cited first, 7 of 7)

- [Select Wisely and Explain: Active Learning and Probabilistic Local Post-hoc Explainability](https://mlsanity.com/paper/2108.06907/) (2021)
- [Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation](https://mlsanity.com/paper/2410.16893/) (2024)
- [Optimizing Posterior Samples for Bayesian Optimization via Rootfinding](https://mlsanity.com/paper/2410.22322/) (2024)
- [Domain Knowledge Injection in Bayesian Search for New Materials](https://mlsanity.com/paper/2311.15162/) (2023)
- [Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?](https://mlsanity.com/paper/2503.03625/) (2025)
- [Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings](https://mlsanity.com/paper/2211.00947/) (2022)
- [mlr3mbo: Bayesian Optimization in R](https://mlsanity.com/paper/2603.29730/) (2026)

## Abstract (arXiv)

Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition function to determine where next to query. Convergence guarantees are only valid when the global optimizer of the acquisition function is found at each round and selected as the next query point. In practice, however, local optimizers of an acquisition function are also used, since searching for the global optimizer is often a non-trivial or time-consuming task. In this paper we consider three popular acquisition functions, PI, EI, and GP-UCB induced by Gaussian process regression. Then we present a performance analysis on the behavior of local optimizers of those acquisition functions, in terms of em instantaneous regrets over global optimizers. We also introduce an analysis, allowing a local optimization method to start from multiple different initial conditions. Numerical experiments confirm the validity of our theoretical analysis.