# Batch Bayesian optimisation via density-ratio estimation with guarantees

arXiv: https://arxiv.org/abs/2209.10715 · HTML: https://mlsanity.com/paper/2209.10715/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 76 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO](https://mlsanity.com/paper/2109.06716/) (2021)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [Optimization-Based Autonomous Racing of 1:43 Scale RC Cars](https://mlsanity.com/paper/1711.07300/) (2017)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior](https://mlsanity.com/paper/1811.09558/) (2018)
- [VIREL: A Variational Inference Framework for Reinforcement Learning](https://mlsanity.com/paper/1811.01132/) (2018)
- [Deep Learning: A Bayesian Perspective](https://mlsanity.com/paper/1706.00473/) (2017)
- [A General Recipe for Likelihood-free Bayesian Optimization](https://mlsanity.com/paper/2206.13035/) (2022)
- [Streaming kernel regression with provably adaptive mean, variance, and regularization](https://mlsanity.com/paper/1708.00768/) (2017)
- [An Efficient Batch Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multi-objective Acquisition Ensemble](https://mlsanity.com/paper/2106.15412/) (2021)
- [Stein Variational Gradient Descent Without Gradient](https://mlsanity.com/paper/1806.02775/) (2018)
- [Computing the racing line using Bayesian optimization](https://mlsanity.com/paper/2002.04794/) (2020)
- [MBORE: Multi-objective Bayesian Optimisation by Density-Ratio Estimation](https://mlsanity.com/paper/2203.16912/) (2022)

## Built on by (most cited first, 9 of 9)

- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Variational Search Distributions](https://mlsanity.com/paper/2409.06142/) (2024)
- [Bayesian Optimisation Against Climate Change: Applications and Benchmarks](https://mlsanity.com/paper/2306.04343/) (2023)
- [Generative Bayesian Optimization: Generative Models as Acquisition Functions](https://mlsanity.com/paper/2510.25240/) (2025)
- [MALIBO: Meta-learning for Likelihood-free Bayesian Optimization](https://mlsanity.com/paper/2307.03565/) (2023)
- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [Kernel-based guarantees for nonlinear parametric models in Bayesian optimization](https://mlsanity.com/paper/2605.13160/) (2026)
- [Density Ratio Estimation-based Bayesian Optimization with Semi-Supervised Learning](https://mlsanity.com/paper/2305.15612/) (2023)
- [Bayesian Optimization by Kernel Regression and Density-based Exploration](https://mlsanity.com/paper/2502.06178/) (2025)

## Abstract (arXiv)

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.