Exploring Exploration in Bayesian Optimization

2025-02-12

AI Summary

Bayesian optimization lacks quantifiable metrics for evaluating the exploratory behavior of acquisition functions, hindering mechanistic analysis of the exploration–exploitation trade-off and cross-function comparison. Method: We propose two computationally tractable exploration metrics—observed Traveling Salesman Distance (oTSPD) and observed Entropy (oEntropy)—that respectively capture geometric coverage and information-theoretic uncertainty in the observed query locations. Contribution/Results: Through extensive black-box function benchmarking and comparative experiments across multiple acquisition functions, we systematically uncover their implicit exploration preferences and empirically demonstrate a non-monotonic relationship between exploration degree and optimization performance. The proposed metrics are interpretable, reproducible, and generalize across tasks, providing both theoretical insight and practical tools for acquisition function design, diagnosis, and selection.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.

Problem

• Quantify exploration in Bayesian optimization
• Measure exploration of acquisition functions
• Link exploration to empirical performance

Innovation

• Novel exploration quantification methods
• Observation traveling salesman distance
• Observation entropy measures exploration