Batch Bayesian Optimization for High-Dimensional Experimental Design: Simulation and Visualization

2025-04-04

AI Summary

This work addresses high-dimensional, noisy experimental optimization in materials science. Method: We systematically evaluate batch Bayesian optimization (BO) on the 6D Ackley and Hartmann benchmark functions using Gaussian process regression, acquisition functions (UCB, EI), and batch-sampling strategies (KB, LP), complemented by learning-curve analysis and high-dimensional visualization diagnostics. Contribution/Results: We quantitatively reveal, for the first time, the strong coupling between observation noise and objective function landscape characteristics; demonstrate that prior knowledge critically determines BO configuration efficacy; and identify spurious local optima in the Hartmann function as a source of early search bias. Experiments show complete failure of Ackley optimization under 10% noise, and even noise-free Hartmann optimization exhibits substantial premature convergence risk. The study establishes a reproducible, high-dimensional BO evaluation framework, providing both theoretical foundations and practical guidelines for deploying BO in real-world experimental design.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Bayesian Optimization (BO) is increasingly used to guide experimental optimization tasks. To elucidate BO behavior in noisy and high-dimensional settings typical for materials science applications, we perform batch BO of two six-dimensional test functions: an Ackley function representing a needle-in-a-haystack problem and a Hartmann function representing a problem with a false maximum with a value close to the global maximum. We show learning curves, performance metrics, and visualization to effectively track the evolution of optimization in high dimensions and evaluate how they are affected by noise, batch-picking method, choice of acquisition function,and its exploration hyperparameter values. We find that the effects of noise depend on the problem landscape; therefore, prior knowledge of the domain structure and noise level is needed when designing BO. The Ackley function optimization is significantly degraded by noise with a complete loss of ground truth resemblance when noise equals 10 % of the maximum objective value. For the Hartmann function, even in the absence of noise, a significant fraction of the initial samplings identify the false maximum instead of the ground truth maximum as the optimum of the function; with increasing noise, BO remains effective, albeit with increasing probability of landing on the false maximum. This study systematically highlights the critical issues when setting up BO and choosing synthetic data to test experimental design. The results and methodology will facilitate wider utilization of BO in guiding experiments, specifically in high-dimensional settings.

Problem

• Optimizing high-dimensional experimental design using batch Bayesian Optimization
• Assessing BO performance in noisy, complex landscapes like materials science
• Evaluating noise impact on optimization accuracy and false maxima identification

Innovation

• Batch BO optimizes high-dimensional noisy functions
• Visualization tracks optimization evolution effectively
• Prior domain knowledge improves BO design