CLUE-BO: Adaptive Language Priors for High-Dimensional Bayesian Optimization

Bayesian optimization (BO) becomes challenging in high dimensions, where limited evaluations make it difficult for Gaussian process surrogates to reliably infer dimension-wise relevance. However, many optimization problems provide semantic descriptions of their decision variables, offering structural information that standard BO does not directly exploit. We introduce CLUE-BO, a language-guided BO framework that uses an LLM to translate task semantics into dimension-specific priors over ARD lengthscales. Rather than treating these semantic priors as fixed or inherently reliable, CLUE-BO continually evaluates them through predictive comparisons between semantic and neutral GPs. Predictive evidence determines when to trigger reflection, whether a revised prior should be activated, and whether optimization should follow semantic or neutral guidance. Across six high-dimensional benchmarks ranging from 30 to 1,003 dimensions, CLUE-BO achieves the best mean final objective on five benchmarks and remains competitive on the sixth. Ablation and trajectory analyses further show that semantic priors complement sparse numerical observations, while evidence-driven control allows unreliable semantic hypotheses to be revised during optimization. These results demonstrate that task semantics can provide useful structural information for high-dimensional BO when observations alone are insufficient.