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Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

Computation · Statistics 2022-08-18 Oskar Gustafsson , Mattias Villani , Pär Stockhammar

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…

Machine Learning · Computer Science 2023-01-18 Quan Nguyen , Kaiwen Wu , Jacob R. Gardner , Roman Garnett

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, robotics. BO usually models the objective function by a Gaussian process (GP), and…

Machine Learning · Statistics 2020-01-22 Chao Qian , Hang Xiong , Ke Xue

Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty…

Artificial Intelligence · Computer Science 2022-02-28 J. Qing , I. Couckuyt , T. Dhaene

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to…

Machine Learning · Statistics 2018-05-16 Mark McLeod , Michael A. Osborne , Stephen J. Roberts

We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a…

Machine Learning · Computer Science 2024-05-30 Wenjie Xu , Wenbin Wang , Yuning Jiang , Bratislav Svetozarevic , Colin N. Jones

Most research in Bayesian optimization (BO) has focused on \emph{direct feedback} scenarios, where one has access to exact values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine…

Machine Learning · Computer Science 2021-09-02 Eero Siivola , Akash Kumar Dhaka , Michael Riis Andersen , Javier Gonzalez , Pablo Garcia Moreno , Aki Vehtari

Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two…

Machine Learning · Statistics 2020-06-17 Jungtaek Kim , Seungjin Choi

Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural…

Machine Learning · Statistics 2026-01-13 Haowei Wang , Jingyi Wang , Zhongxiang Dai , Nai-Yuan Chiang , Szu Hui Ng , Cosmin G. Petra

Performing multi-objective Bayesian optimisation by scalarising the objectives avoids the computation of expensive multi-dimensional integral-based acquisition functions, instead of allowing one-dimensional standard acquisition…

Machine Learning · Computer Science 2021-04-13 Clym Stock-Williams , Tinkle Chugh , Alma Rahat , Wei Yu

We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function…

Machine Learning · Statistics 2025-11-13 Felix Huber , Sebastian Rojas Gonzalez , Raul Astudillo

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…

Machine Learning · Statistics 2016-11-16 Matthias Poloczek , Jialei Wang , Peter I. Frazier

Incorporating user preferences into multi-objective Bayesian optimization (MOBO) allows for personalization of the optimization procedure. Preferences are often abstracted in the form of an unknown utility function, estimated through…

Machine Learning · Computer Science 2025-03-19 Joshua Hang Sai Ip , Ankush Chakrabarty , Ali Mesbah , Diego Romeres

Many contemporary machine learning models require extensive tuning of hyperparameters to perform well. A variety of methods, such as Bayesian optimization, have been developed to automate and expedite this process. However, tuning remains…

Machine Learning · Computer Science 2020-02-25 Setareh Ariafar , Zelda Mariet , Ehsan Elhamifar , Dana Brooks , Jennifer Dy , Jasper Snoek

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors…

Machine Learning · Statistics 2025-02-13 Jingyi Wang , Haowei Wang , Nai-Yuan Chiang , Cosmin G. Petra

We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number…

Machine Learning · Computer Science 2020-11-24 Syrine Belakaria , Aryan Deshwal , Janardhan Rao Doppa

We consider a multi-objective optimization problem with objective functions that are expensive to evaluate. The decision maker (DM) has unknown preferences, and so the standard approach is to generate an approximation of the Pareto front…

Machine Learning · Computer Science 2021-05-28 Juan Ungredda , Mariapia Marchi , Teresa Montrone , Juergen Branke

Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian…

Machine Learning · Computer Science 2024-02-28 Arun Kumar A , Alistair Shilton , Sunil Gupta , Santu Rana , Stewart Greenhill , Svetha Venkatesh

Many real-world optimisation problems are defined over both categorical and continuous variables, yet efficient optimisation methods such asBayesian Optimisation (BO) are not designed tohandle such mixed-variable search spaces. Recent…

Machine Learning · Statistics 2022-02-18 Yan Zuo , Amir Dezfouli , Iadine Chades , David Alexander , Benjamin Ward Muir

Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the…

Machine Learning · Computer Science 2024-11-11 Jungtaek Kim