# Batch Bayesian Optimization via Local Penalization

arXiv: https://arxiv.org/abs/1505.08052 · HTML: https://mlsanity.com/paper/1505.08052/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2015.

## Built on by (most cited first, 30 of 104)

- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [OpenBox: A Generalized Black-box Optimization Service](https://mlsanity.com/paper/2106.00421/) (2021)
- [GAUCHE: A Library for Gaussian Processes in Chemistry](https://mlsanity.com/paper/2212.04450/) (2022)
- [PriorBand: Practical Hyperparameter Optimization in the Age of Deep Learning](https://mlsanity.com/paper/2306.12370/) (2023)
- [Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes](https://mlsanity.com/paper/2110.11665/) (2021)
- [Bayesian Optimization for Cascade-type Multi-stage Processes](https://mlsanity.com/paper/2111.08330/) (2021)
- [Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization](https://mlsanity.com/paper/2211.06149/) (2022)
- [Framework and Benchmarks for Combinatorial and Mixed-variable Bayesian Optimization](https://mlsanity.com/paper/2306.09803/) (2023)
- [SnAKe: Bayesian Optimization with Pathwise Exploration](https://mlsanity.com/paper/2202.00060/) (2022)
- [Adaptive machine learning for protein engineering](https://mlsanity.com/paper/2106.05466/) (2021)
- [An Efficient Batch Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multi-objective Acquisition Ensemble](https://mlsanity.com/paper/2106.15412/) (2021)
- [Faster Improvement Rate Population Based Training](https://mlsanity.com/paper/2109.13800/) (2021)
- [Hyper-Tune: Towards Efficient Hyper-parameter Tuning at Scale](https://mlsanity.com/paper/2201.06834/) (2022)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Inversion-based Latent Bayesian Optimization](https://mlsanity.com/paper/2411.05330/) (2024)
- [Safe and Efficient Model-free Adaptive Control via Bayesian Optimization](https://mlsanity.com/paper/2101.07825/) (2021)
- [Bayesian Optimization under Stochastic Delayed Feedback](https://mlsanity.com/paper/2206.09341/) (2022)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [A portfolio approach to massively parallel Bayesian optimization](https://mlsanity.com/paper/2110.09334/) (2021)
- [Batch Bayesian optimisation via density-ratio estimation with guarantees](https://mlsanity.com/paper/2209.10715/) (2022)
- [OpenBox: A Python Toolkit for Generalized Black-box Optimization](https://mlsanity.com/paper/2304.13339/) (2023)
- [Exploring Exploration in Bayesian Optimization](https://mlsanity.com/paper/2502.08208/) (2025)
- [Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/2107.14465/) (2021)
- [Machine Learning with Knowledge Constraints for Process Optimization of Open-Air Perovskite Solar Cell Manufacturing](https://mlsanity.com/paper/2110.01387/) (2021)

## Abstract (arXiv)

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These facilities could be computational or physical facets of the process being optimized. E.g. in biological experiments many experimental set ups allow several samples to be simultaneously processed. Batch methods, however, require modeling of the interaction between the evaluations in the batch, which can be expensive in complex scenarios. We investigate a simple heuristic based on an estimate of the Lipschitz constant that captures the most important aspect of this interaction (i.e. local repulsion) at negligible computational overhead. The resulting algorithm compares well, in running time, with much more elaborate alternatives. The approach assumes that the function of interest, f, is a Lipschitz continuous function. A wrap-loop around the acquisition function is used to collect batches of points of certain size minimizing the non-parallelizable computational effort. The speed-up of our method with respect to previous approaches is significant in a set of computationally expensive experiments.