Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search

High-dimensional Bayesian optimization (HDBO) seeks sample-efficient optimization when the number of variables is large relative to the evaluation budget. Recent LLM-based and agentic BO methods incorporate task knowledge and adapt search decisions during a run, but have primarily been evaluated on low- and moderate-dimensional problems. We ask whether this paradigm can transfer to the higher-dimensional regime. Our experiments show that these methods do not remain reliable in the high-dimensional regime, where the challenge is not only where to evaluate, but also which modeling assumption and search geometry to use when the objective's useful structure is unknown. We therefore introduce HERA, a Hypothesis- and Evidence-guided Research Agent, which manages revisable search hypotheses, and PRISM, which executes specialized optimizers. HERA remains competitive with strong classical HDBO methods on metadata-free synthetic functions. Across diverse real-world tasks, it achieves the best mean final objective on most benchmarks, outperforming strong classical and recent LLM-based or agentic methods. Further analyses characterize how structural evidence, task metadata, and decision frequency shape its behavior and performance.