# Batched Energy-Entropy acquisition for Bayesian Optimization

arXiv: https://arxiv.org/abs/2410.08804 · HTML: https://mlsanity.com/paper/2410.08804/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 61 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 30 of 34)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration](https://mlsanity.com/paper/1304.5350/) (2013)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [GLASSES: Relieving The Myopia Of Bayesian Optimisation](https://mlsanity.com/paper/1510.06299/) (2015)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Batched Gaussian Process Bandit Optimization via Determinantal Point Processes](https://mlsanity.com/paper/1611.04088/) (2016)
- [Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions](https://mlsanity.com/paper/1511.07130/) (2015)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [MUMBO: MUlti-task Max-value Bayesian Optimization](https://mlsanity.com/paper/2006.12093/) (2020)
- [Parallelizing Thompson Sampling](https://mlsanity.com/paper/2106.01420/) (2021)

## Built on by (most cited first, 2 of 2)

- [Generative Bayesian Optimization: Generative Models as Acquisition Functions](https://mlsanity.com/paper/2510.25240/) (2025)
- [In-Context Batch Black-box Optimization via Flow Matching](https://mlsanity.com/paper/2610.20138/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function for BO with Gaussian processes that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing methods.