Calibrating LLM Guidance for Acquisition Selection in Bayesian Optimization

Bayesian optimization (BO) is a sample-efficient approach to black-box optimization, but its performance often depends on task-specific design choices, including acquisition functions and trust region methods. Identifying effective configurations often requires human expertise or substantial manual experimentation. Large language models (LLMs) offer a promising approach to automatically recommend these choices using task descriptions and optimization histories. However, it is reportedly difficult for LLMs to track long interaction histories efficiently, which can undermine the reliability of their recommendations for complex tasks. We propose LLM-Prior-Informed Gaussian Upper Confidence Bound (LPG-UCB), a framework that combines LLM guidance with empirical feedback to adaptively select acquisition functions. LPG-UCB encodes LLM recommendations as priors over acquisition function preferences and updates these preferences through Bayesian inference as the BO loop proceeds. This Bayesian update mechanism leverages summary statistics from the BO trajectory to refine and calibrate LLM guidance, reducing reliance on the accuracy of individual LLM recommendations. We model LPG-UCB as a non-stationary rotting-bandit framework, and derive an expected cumulative regret bound, which grows sublinearly under appropriate conditions. Extensive experiments on diverse synthetic benchmarks demonstrate faster convergence than competing LLM-based selection methods. LPG-UCB also achieves competitive performance on a high-dimensional black-box optimization problem.