Bayesian Optimization with Rich Auxiliary Information via LLMs

Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, yet it typically reduces each expensive experiment to an input and its objective value, discarding much of the information the experiment produces. Such auxiliary information can include training curves in hyperparameter optimization, expert notes and images in scientific experimentation, or known facts about the specific optimization problem. Leveraging the ability of large language models (LLMs) to process diverse and unstructured information, we introduce two methods: AuxBO-Evolve, which uses auxiliary information to evolve beliefs over the location of the optimum, and AuxBO-Vicinity, which uses it to locally guide the acquisition function. Across synthetic tasks, hyperparameter optimization benchmarks, and a nuclear fusion task with unstructured scientist-written logs, our methods consistently improve optimization performance and outperform standard BO and existing LLM-based approaches. We further find that LLMs provide more effective probabilistic guidance when modeling likely maximizer locations rather than objective values pointwise. Overall, our results demonstrate that exploiting rich information beyond standard (x, y) interactions can substantially improve BO performance.