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We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of…

Machine Learning · Computer Science 2021-03-19 Carlos Ansotegui , Meinolf Sellmann , Tapan Shah , Kevin Tierney

We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible…

Artificial Intelligence · Computer Science 2020-09-10 Nikolaus Hansen , Anne Auger , Raymond Ros , Olaf Mersmann , Tea Tušar , Dimo Brockhoff

A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…

Mathematical Software · Computer Science 2018-06-19 Jan Verschelde

One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by…

Optimization and Control · Mathematics 2023-04-04 Mickael Binois , Nicholson Collier , Jonathan Ozik

Black-box optimization (BBO) has a broad range of applications, including automatic machine learning, experimental design, and database knob tuning. However, users still face challenges when applying BBO methods to their problems at hand…

Machine Learning · Computer Science 2024-05-17 Huaijun Jiang , Yu Shen , Yang Li , Beicheng Xu , Sixian Du , Wentao Zhang , Ce Zhang , Bin Cui

We present a budget-free experimental setup and procedure for benchmarking numericaloptimization algorithms in a black-box scenario. This procedure can be applied with the COCO benchmarking platform. We describe initialization of and input…

Artificial Intelligence · Computer Science 2016-05-20 Nikolaus Hansen , Tea Tusar , Olaf Mersmann , Anne Auger , Dimo Brockhoff

In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some…

Neural and Evolutionary Computing · Computer Science 2026-01-26 Catalin-Viorel Dinu , Diederick Vermetten , Carola Doerr

Black-box optimization (BBO) has a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. However, it remains a challenge for users to apply BBO methods to their problems at hand…

Machine Learning · Computer Science 2021-11-05 Yang Li , Yu Shen , Wentao Zhang , Yuanwei Chen , Huaijun Jiang , Mingchao Liu , Jiawei Jiang , Jinyang Gao , Wentao Wu , Zhi Yang , Ce Zhang , Bin Cui

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…

Mathematical Software · Computer Science 2021-04-30 Ruoxi Wang , Chao Chen , Jonghyun Lee , Eric Darve

Black-box optimization is often encountered for decision-making in complex systems management, where the knowledge of system is limited. Under these circumstances, it is essential to balance the utilization of new information with…

Computation · Statistics 2025-01-15 Teng Lian , Jian-Qiang Hu , Yuhang Wu , Zeyu Zheng

Black box optimization requires specifying a search space to explore for solutions, e.g. a d-dimensional compact space, and this choice is critical for getting the best results at a reasonable budget. Unfortunately, determining a high…

Machine Learning · Computer Science 2021-12-20 Setareh Ariafar , Justin Gilmer , Zachary Nado , Jasper Snoek , Rodolphe Jenatton , George E. Dahl

The `spotoptim` package implements surrogate-model-based optimization of expensive black-box functions in Python. Building on two decades of Sequential Parameter Optimization (SPO) methodology, it provides a Kriging-based optimization loop…

Machine Learning · Computer Science 2026-04-16 Thomas Bartz-Beielstein

We present a simple and powerful algorithm for parallel black box optimization called Successive Halving and Classification (SHAC). The algorithm operates in $K$ stages of parallel function evaluations and trains a cascade of binary…

Computer Vision and Pattern Recognition · Computer Science 2018-05-30 Manoj Kumar , George E. Dahl , Vijay Vasudevan , Mohammad Norouzi

Parallel black box optimization consists in estimating the optimum of a function using $\lambda$ parallel evaluations of $f$. Averaging the $\mu$ best individuals among the $\lambda$ evaluations is known to provide better estimates of the…

Optimization and Control · Mathematics 2021-08-11 Laurent Meunier , Iskander Legheraba , Yann Chevaleyre , Olivier Teytaud

This document details the rationales behind assessing the performance of numerical black-box optimizers on multi-objective problems within the COCO platform and in particular on the biobjective test suite bbob-biobj. The evaluation is based…

Neural and Evolutionary Computing · Computer Science 2016-05-09 Dimo Brockhoff , Tea Tušar , Dejan Tušar , Tobias Wagner , Nikolaus Hansen , Anne Auger

The use of blackbox solvers inside neural networks is a relatively new area which aims to improve neural network performance by including proven, efficient solvers for complex problems. Existing work has created methods for learning…

Machine Learning · Computer Science 2020-06-09 T. J. Wilder

Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to…

Black-box optimization (BBO) can be used to optimize functions whose analytic form is unknown. A common approach to realising BBO is to learn a surrogate model which approximates the target black-box function which can then be solved via…

Machine Learning · Computer Science 2023-02-10 Jonas Nüßlein , Christoph Roch , Thomas Gabor , Jonas Stein , Claudia Linnhoff-Popien , Sebastian Feld

When faced with a limited budget of function evaluations, state-of-the-art black-box optimization (BBO) solvers struggle to obtain globally, or sometimes even locally, optimal solutions. In such cases, one may pursue solution polishing,…

Optimization and Control · Mathematics 2024-02-20 Dimitri Papageorgiou , Jan Kronqvist , Asha Ramanujam , James Kor , Youngdae Kim , Can Li

Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…

Machine Learning · Computer Science 2023-12-29 Keisuke Morita , Yoshihiko Nishikawa , Masayuki Ohzeki
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