# B3O: Scalable Boltzmann Batch Bayesian Optimization

arXiv: https://arxiv.org/abs/2606.30228 · HTML: https://mlsanity.com/paper/2606.30228/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Boltzmann Exploration Done Right](https://mlsanity.com/paper/1705.10257/) (2017)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Scalable Thompson Sampling using Sparse Gaussian Process Models](https://mlsanity.com/paper/2006.05356/) (2020)
- [Batched Gaussian Process Bandit Optimization via Determinantal Point Processes](https://mlsanity.com/paper/1611.04088/) (2016)
- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes](https://mlsanity.com/paper/2110.11665/) (2021)
- [Multi-Objective Constrained Optimization for Energy Applications via Tree Ensembles](https://mlsanity.com/paper/2111.03140/) (2021)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Fully Distributed Bayesian Optimization with Stochastic Policies](https://mlsanity.com/paper/1902.09992/) (2019)
- [Black-box density function estimation using recursive partitioning](https://mlsanity.com/paper/2010.13632/) (2020)
- [Stein Boltzmann Sampling: A Variational Approach for Global Optimization](https://mlsanity.com/paper/2402.04689/) (2024)

## Abstract (arXiv)

Modern engineering workflows increasingly rely on massive parallel simulation, driving the need for scalable, large-batch Bayesian Optimization (BO). Existing batch BO methods, however, incur large computational cost or rely on approximations that erode batch diversity. We propose B3O (Boltzmann Batch Bayesian Optimization), a framework that reframes batch generation as a pure sampling problem: drawing samples directly from the Boltzmann distribution defined by the acquisition function avoids the bottlenecks of existing large-batch methods. Theoretically, we prove that queries sampled from this distribution incur only negligible additional regret. Empirically, B3O outperforms existing batch BO methods on standard synthetic benchmarks and adapts robustly across complex applied tasks, including multi-objective electrode design and mixed-variable race car configuration.