# Maximizing acquisition functions for Bayesian optimization

arXiv: https://arxiv.org/abs/1805.10196 · HTML: https://mlsanity.com/paper/1805.10196/

## Key facts

- Cited by 114 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2018.

## Built on by (most cited first, 30 of 114)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization](https://mlsanity.com/paper/2210.10199/) (2022)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [BORE: Bayesian Optimization by Density-Ratio Estimation](https://mlsanity.com/paper/2102.09009/) (2021)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [A General Framework for User-Guided Bayesian Optimization](https://mlsanity.com/paper/2311.14645/) (2023)
- [Model Predictive Task Sampling for Efficient and Robust Adaptation](https://mlsanity.com/paper/2501.11039/) (2025)
- [Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination](https://mlsanity.com/paper/2206.04734/) (2022)
- [A General Recipe for Likelihood-free Bayesian Optimization](https://mlsanity.com/paper/2206.13035/) (2022)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Quick-Tune: Quickly Learning Which Pretrained Model to Finetune and How](https://mlsanity.com/paper/2306.03828/) (2023)
- [Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials](https://mlsanity.com/paper/2210.04225/) (2022)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces](https://mlsanity.com/paper/2301.13088/) (2023)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Zero-Shot AutoML with Pretrained Models](https://mlsanity.com/paper/2206.08476/) (2022)
- [Reinforced In-Context Black-Box Optimization](https://mlsanity.com/paper/2402.17423/) (2024)
- [Adaptive machine learning for protein engineering](https://mlsanity.com/paper/2106.05466/) (2021)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Generalizing Bayesian Optimization with Decision-theoretic Entropies](https://mlsanity.com/paper/2210.01383/) (2022)
- [Stopping Bayesian Optimization with Probabilistic Regret Bounds](https://mlsanity.com/paper/2402.16811/) (2024)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)

## Abstract (arXiv)

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose properties not only facilitate but justify use of greedy approaches for their maximization.