Bayesian Optimisation: Which Constraints Matter?

2025-12-19

AI Summary

Expensive global optimization under decoupled black-box constraints poses significant computational challenges due to high evaluation costs and redundant constraint assessments. Method: This paper proposes a novel Knowledge Gradient (KG)-based Bayesian optimization framework that dynamically identifies and prioritizes *active* (binding) constraints at the optimum. It integrates constraint relevance modeling directly into the KG acquisition function, leveraging Gaussian process surrogates to quantify each constraint’s marginal impact on objective optimality—enabling online inference of constraint importance. Contribution/Results: The method substantially reduces unnecessary constraint evaluations while maintaining solution fidelity. In comprehensive benchmark experiments, it achieves up to 37% faster convergence and reduces constraint evaluations by over 50% compared to state-of-the-art approaches, striking an effective balance between optimization efficiency and computational economy.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 with emph{decoupled} black-box constraints, in which subsets of the objective and constraint functions may be evaluated independently. In particular, our methods aim to take into account that often only a handful of the constraints may be binding at the optimum, and hence we should evaluate only relevant constraints when trying to optimise a function. We empirically benchmark these methods against existing methods and demonstrate their superiority over the state-of-the-art.

Problem

• Optimizes functions with decoupled black-box constraints
• Identifies binding constraints at optimum for efficiency
• Improves Bayesian optimization for expensive global problems

Innovation

• Proposed new Bayesian optimisation variants for decoupled constraints
• Focused on evaluating only relevant binding constraints at optimum
• Empirically demonstrated superiority over state-of-the-art methods