Large Language Models as Prior Elicitors for Sample-Efficient Black-Box Optimization

Many scientific and engineering applications require optimizing complex decisions whose outcomes can only be evaluated through costly simulations, experiments, or high-fidelity models, giving rise to black-box optimization (BBO) under tight evaluation budgets. Existing BBO methods typically learn from objective evaluations collected on the target task and therefore rely heavily on costly observation-driven exploration. Large language models (LLMs), with broad cross-domain knowledge, offer a potential opportunities to alleviate this dependence. This study introduces a different perspective on using LLMs for BBO: rather than using LLMs to assist sampling, we elicit embedded domain knowledge of LLMs to explicitly form a probabilistic distribution over objective functions. Specifically, we develop an LLM-enhanced Bayesian optimization framework that first elicits a probabilistic prior over the objective function from LLMs and then incorporates this prior into Bayesian optimization. The key idea is to develop an agentic preference elicitation method, where an LLM agent is established to analyze the problem context and to generate pairwise preferences between candidate solutions, thereby deriving a probabilistic distribution through Bayesian preference learning before expensive evaluations are collected. Theoretically, we show that the elicited distribution contracts predictive uncertainty and information gain and, under an explicit alignment condition, yields a no-larger finite-budget GP-LCB simple-regret bound than the reference prior. We further establish controlled sensitivity to corrupted preferences and show that an initially biased prior can be corrected as sufficiently informative objective observations accumulate. Experiments on six real-world benchmarks demonstrate improved sample efficiency, with the largest gains under limited evaluation budgets.