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We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence…

Machine Learning · Computer Science 2010-12-14 Eric Brochu , Vlad M. Cora , Nando de Freitas

Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in…

Applications · Statistics 2025-12-04 Thomas A. Archbold , Ieva Kazlauskaite , Fehmi Cirak

Bayesian optimization has been shown to be a powerful tool for solving black box problems during online accelerator optimization. The major advantage of Bayesian based optimization techniques is the ability to include prior information…

Accelerator Physics · Physics 2022-11-17 Connie Xu , Ryan Roussel , Auralee Edelen

This paper investigates a new class of modifier-adaptation schemes to overcome plant-model mismatch in real-time optimization of uncertain processes. The main contribution lies in the integration of concepts from the areas of Bayesian…

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

Bayesian optimization is a powerful paradigm to optimize black-box functions based on scarce and noisy data. Its data efficiency can be further improved by transfer learning from related tasks. While recent transfer models meta-learn a…

Bayesian optimisation is a sample efficient method for finding a global optimum of expensive black-box objective functions. Historic datasets from related problems can be exploited to help improve performance of Bayesian optimisation by…

Machine Learning · Computer Science 2026-01-23 Natasha Trinkle , Huong Ha , Jeffrey Chan

Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the…

Machine Learning · Statistics 2019-10-17 Valerio Perrone , Iaroslav Shcherbatyi , Rodolphe Jenatton , Cedric Archambeau , Matthias Seeger

Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in…

Machine Learning · Computer Science 2026-03-03 Qiyu Wei , Haowei Wang , Richard Allmendinger , Mauricio A. Álvarez

A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare…

Machine Learning · Computer Science 2026-05-15 Leonard Papenmeier , Nuojin Cheng , Stephen Becker , Luigi Nardi

We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active…

Machine Learning · Statistics 2021-04-12 Antoine Blanchard , Themistoklis Sapsis

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…

Machine Learning · Computer Science 2020-06-25 Alma Rahat , Michael Wood

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Machine Learning · Statistics 2012-12-04 Xun Huan , Youssef M. Marzouk

We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…

Machine Learning · Computer Science 2026-02-04 Paul Brunzema , Sebastian Trimpe

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

Machine Learning · Computer Science 2025-10-09 Akash Yadav , Ruda Zhang

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by…

Machine Learning · Computer Science 2023-12-22 Xiaobin Huang , Lei Song , Ke Xue , Chao Qian

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

Machine Learning · Computer Science 2021-06-15 Meet P. Vadera , Soumya Ghosh , Kenney Ng , Benjamin M. Marlin

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to…

Machine Learning · Statistics 2026-05-15 Nuojin Cheng , Leonard Papenmeier , Stephen Becker , Luigi Nardi

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

Machine Learning · Statistics 2014-07-01 Ziyu Wang , Nando de Freitas

In Bayesian optimization (BO) for expensive black-box optimization tasks, acquisition function (AF) guides sequential sampling and plays a pivotal role for efficient convergence to better optima. Prevailing AFs usually rely on artificial…

Machine Learning · Computer Science 2022-10-04 Zijing Liu , Xiyao Qu , Xuejun Liu , Hongqiang Lyu