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Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of $\mathcal{R}^d$, by using a Gaussian process (GP) as a surrogate model…

Machine Learning · Statistics 2018-09-24 Eero Siivola , Aki Vehtari , Jarno Vanhatalo , Javier González , Michael Riis Andersen

Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence towards…

Machine Learning · Computer Science 2025-10-23 Ruiyao Miao , Junren Xiao , Shiya Tsang , Hui Xiong , Yingnian Wu

Bayesian optimization (BO) is widely adopted in black-box optimization problems and it relies on a surrogate model to approximate the black-box response function. With the increasing number of black-box optimization tasks solved and even…

Machine Learning · Computer Science 2023-08-10 Wenlong Lyu , Shoubo Hu , Jie Chuai , Zhitang Chen

Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function. To ensure the quality of the model, transfer…

Machine Learning · Computer Science 2024-02-15 Zhou Fan , Xinran Han , Zi Wang

Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…

Machine Learning · Computer Science 2022-02-09 Jaeyeon Ahn , Taehyeon Kim , Seyoung Yun

Model-based Bayesian reinforcement learning has generated significant interest in the AI community as it provides an elegant solution to the optimal exploration-exploitation tradeoff in classical reinforcement learning. Unfortunately, the…

Artificial Intelligence · Computer Science 2012-06-18 Stephane Ross , Joelle Pineau

We introduce the algorithm Bayesian Optimization (BO) with Fictitious Play (BOFiP) for the optimization of high dimensional black box functions. BOFiP decomposes the original, high dimensional, space into several sub-spaces defined by…

Machine Learning · Computer Science 2021-10-11 L. Mathesen , G. Pedrielli , R. L. Smith

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO…

Machine Learning · Computer Science 2019-03-19 Kirthevasan Kandasamy , Willie Neiswanger , Jeff Schneider , Barnabas Poczos , Eric Xing

Optimizing expensive black-box objectives over mixed search spaces is a common challenge across the natural sciences. Bayesian optimization (BO) offers sample-efficient strategies through probabilistic surrogate models and acquisition…

Machine Learning · Computer Science 2026-04-10 Yuhao Zhang , Ti John , Matthias Stosiek , Patrick Rinke

We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design…

Machine Learning · Computer Science 2021-12-03 Aryan Deshwal , Syrine Belakaria , Janardhan Rao Doppa

Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…

Machine Learning · Statistics 2020-11-04 Michael Pearce , Janis Klaise , Matthew Groves

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function…

Machine Learning · Computer Science 2023-12-25 Alexandre Maraval , Matthieu Zimmer , Antoine Grosnit , Haitham Bou Ammar

Bayesian Optimization (BO) in high-dimensional spaces remains fundamentally limited by the curse of dimensionality and the rigidity of global low-dimensional assumptions. While Random EMbedding Bayesian Optimization (REMBO) mitigates this…

Machine Learning · Statistics 2025-05-19 Yuejiang Wen , Paul D. Franzon

Bayesian optimization (BO) is a powerful black-box optimization framework that looks to efficiently learn the global optimum of an unknown system by systematically trading-off between exploration and exploitation. However, the use of BO as…

Optimization and Control · Mathematics 2023-03-28 Dinesh Krishnamoorthy , Joel A. Paulson

The tuning of hyperparameters becomes increasingly important as machine learning (ML) models have been extensively applied in data mining applications. Among various approaches, Bayesian optimization (BO) is a successful methodology to tune…

Machine Learning · Computer Science 2022-06-07 Yang Li , Yu Shen , Huaijun Jiang , Tianyi Bai , Wentao Zhang , Ce Zhang , Bin Cui

Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…

Machine Learning · Computer Science 2025-12-22 Xietao Wang Lin , Juan Ungredda , Max Butler , James Town , Alma Rahat , Hemant Singh , Juergen Branke

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of…

Machine Learning · Computer Science 2025-07-08 Taeyoung Yun , Kiyoung Om , Jaewoo Lee , Sujin Yun , Jinkyoo Park

Bayesian optimization (BO) is a prominent approach to optimizing expensive-to-evaluate black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to a surging…

Machine Learning · Computer Science 2020-10-23 Zhongxiang Dai , Kian Hsiang Low , Patrick Jaillet

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…

Machine Learning · Statistics 2020-02-04 Eduardo C. Garrido-Merchán , Daniel Hernández-Lobato

Bayesian optimization (BO) is a widely used iterative algorithm for optimizing black-box functions. Each iteration requires maximizing an acquisition function, such as the upper confidence bound (UCB) or a sample path from the Gaussian…

Machine Learning · Statistics 2025-06-16 Hwanwoo Kim , Chong Liu , Yuxin Chen