PHEBO: Predictive Feedback-Driven Hypothesis Evolution for Bayesian Optimization

Bayesian optimization (BO) offers a sample-efficient framework for scientific optimization with costly evaluations. Large language models (LLMs) can enrich this framework by proposing domain-informed hypotheses, but how to assess their reliability, translate them into numerical guidance, and revise them as evidence accumulates remains a key challenge. This paper introduces PHEBO, an LLM-enhanced BO framework in which predictive feedback drives the evolution of hypotheses population. These hypotheses are encoded in conditional Gaussian process models that quantify their numerical effects. Prospective forecast evaluation updates hypothesis credits, which govern acquisition and hypothesis selection. At scheduled interventions, the LLM uses accumulated observations and credits to revise existing hypotheses, recombine them, and propose new ones, closing the loop between domain reasoning and numerical optimization. Rather than relying on LLMs for in-context numerical prediction or self-reported confidence, PHEBO focuses the LLM on identifying and revising qualitative trends and relationships, guided by empirical predictive feedback. Across four offline scientific optimization tasks spanning analytical chemistry, materials design, and organic photovoltaics, PHEBO achieves better overall performance against GP-based and LLM-enhanced BO baselines. Beyond numerical optimization, the resulting domain beliefs, refined through observation and reasoning, have the potential to inform scientific discovery and support other LLM-enhanced workflows.