Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?

2025-03-05

AI Summary

This work investigates how the choice of acquisition function optimizer affects convergence and efficiency in Bayesian optimization. We systematically compare the deterministic global optimizer MAiNGO against local (L-BFGS-B) and stochastic global (multi-start) methods across varying acquisition function characteristics—specifically, exploration- versus exploitation-dominant behavior—and data diversity regimes. Evaluation metrics include probability of converging to the global optimum, robustness, and computational overhead. Our key finding is that the exploration/exploitation bias of the acquisition function fundamentally determines whether global optimization is necessary: under strong exploitation, MAiNGO significantly reduces iteration count but risks premature convergence in low-data regimes; under exploration, all three optimizers achieve comparable convergence rates, though MAiNGO incurs marginally higher runtime. Crucially, we challenge the “more accurate is always better” paradigm by demonstrating that suboptimal optimization can yield superior practical performance under specific conditions. This study provides both theoretical insight and empirical guidance for acquisition function solver selection in Bayesian optimization.

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Bayesian Optimization (BO) with Gaussian Processes relies on optimizing an acquisition function to determine sampling. We investigate the advantages and disadvantages of using a deterministic global solver (MAiNGO) compared to conventional local and stochastic global solvers (L-BFGS-B and multi-start, respectively) for the optimization of the acquisition function. For CPU efficiency, we set a time limit for MAiNGO, taking the best point as optimal. We perform repeated numerical experiments, initially using the Muller-Brown potential as a benchmark function, utilizing the lower confidence bound acquisition function; we further validate our findings with three alternative benchmark functions. Statistical analysis reveals that when the acquisition function is more exploitative (as opposed to exploratory), BO with MAiNGO converges in fewer iterations than with the local solvers. However, when the dataset lacks diversity, or when the acquisition function is overly exploitative, BO with MAiNGO, compared to the local solvers, is more likely to converge to a local rather than a global ly near-optimal solution of the black-box function. L-BFGS-B and multi-start mitigate this risk in BO by introducing stochasticity in the selection of the next sampling point, which enhances the exploration of uncharted regions in the search space and reduces dependence on acquisition function hyperparameters. Ultimately, suboptimal optimization of poorly chosen acquisition functions may be preferable to their optimal solution. When the acquisition function is more exploratory, BO with MAiNGO, multi-start, and L-BFGS-B achieve comparable probabilities of convergence to a globally near-optimal solution (although BO with MAiNGO may require more iterations to converge under these conditions).

Problem

• Compare deterministic global solver MAiNGO with local and stochastic solvers in Bayesian Optimization.
• Analyze impact of acquisition function type on convergence and solution quality.
• Evaluate trade-offs between exploration and exploitation in optimizing acquisition functions.

Innovation

• Deterministic global solver MAiNGO optimizes acquisition function.
• MAiNGO converges faster in exploitative scenarios.
• Stochastic solvers enhance exploration in diverse datasets.