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We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with decoupled constraints, in which…

This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the…

Machine Learning · Statistics 2021-04-15 Eduardo C. Garrido-Merchán , Daniel Hernández-Lobato

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the…

Machine Learning · Statistics 2014-06-11 José Miguel Hernández-Lobato , Matthew W. Hoffman , Zoubin Ghahramani

Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the…

Machine Learning · Statistics 2018-08-06 Zi Wang , Stefanie Jegelka

This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints…

Optimization and Control · Mathematics 2025-03-07 Qifeng Li

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and…

Machine Learning · Statistics 2015-03-06 Bobak Shahriari , Ziyu Wang , Matthew W. Hoffman , Alexandre Bouchard-Côté , Nando de Freitas

Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the…

Machine Learning · Statistics 2021-07-02 Eduardo C. Garrido-Merchán , Daniel Hernández-Lobato

Bayesian optimization is a widely used technique for optimizing black-box functions, with Expected Improvement (EI) being the most commonly utilized acquisition function in this domain. While EI is often viewed as distinct from other…

Machine Learning · Statistics 2025-03-11 Nuojin Cheng , Stephen Becker

Information-theoretic Bayesian optimization techniques have become popular for optimizing expensive-to-evaluate black-box functions due to their non-myopic qualities. Entropy Search and Predictive Entropy Search both consider the entropy…

Machine Learning · Computer Science 2023-01-18 Carl Hvarfner , Frank Hutter , Luigi Nardi

We develop parallel predictive entropy search (PPES), a novel algorithm for Bayesian optimization of expensive black-box objective functions. At each iteration, PPES aims to select a batch of points which will maximize the information gain…

Machine Learning · Computer Science 2015-11-24 Amar Shah , Zoubin Ghahramani

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor…

Machine Learning · Computer Science 2023-12-27 Shengbo Wang , Ke Li

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient…

Machine Learning · Computer Science 2025-11-25 David Stenger , Armin Lindicke , Alexander von Rohr , Sebastian Trimpe

We present MESMOC+, an improved version of Max-value Entropy search for Multi-Objective Bayesian optimization with Constraints (MESMOC). MESMOC+ can be used to solve constrained multi-objective problems when the objectives and the…

This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…

Optimization and Control · Mathematics 2026-04-22 Qifeng Li

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

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

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

This letter considers optimizing user association in a heterogeneous network via utility maximization, which is a combinatorial optimization problem due to integer constraints. Different from existing solutions based on convex optimization,…

Information Theory · Computer Science 2018-06-12 Xietian Huang , Wei Xu , Guo Xie , Shi Jin , Xiaohu You

When learning to ride a bike, a child falls down a number of times before achieving the first success. As falling down usually has only mild consequences, it can be seen as a tolerable failure in exchange for a faster learning process, as…

Machine Learning · Computer Science 2020-05-18 Alonso Marco , Alexander von Rohr , Dominik Baumann , José Miguel Hernández-Lobato , Sebastian Trimpe

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous…

Artificial Intelligence · Computer Science 2012-10-19 Tom Claassen , Tom Heskes
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