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

Bayesian optimization (BO) has become the standard tool for sample-efficient optimization and owes its efficiency to uncertainty-aware search driven by generic statistical priors. Richer domain priors can improve BO in principle, but encoding them through tailored kernels or problem structure is difficult and rarely done in practice. LLMs can help sidestep this difficulty by making informal priors from natural language, code, and documentation directly available to the optimizer. However, existing LLM-based BO methods either insert the LLM into a fixed role (surrogate, acquisition proxy, or configuration interface) or hand it broad control, sacrificing the systematic exploration that makes BO reliable. We introduce agentic Bayesian optimization: a paradigm in which an LLM agent is the central decision maker in the BO loop while a Bayesian backend provides the uncertainty-aware optimization substrate. The agent configures the problem, queries the backend, selects and commits evaluations, and can revise the optimization strategy during the run by tightening bounds, switching acquisition functions, proposing targeted evaluations, or even reframing the problem following new instructions or observed evidence. We instantiate this idea in Sara, a surrogate-augmented autoresearch agent, and lenz, a modular BoTorch-based backend that the agent can inspect and modify through a structured interface. Across synthetic and real-world benchmarks, Sara preserves the reliability of state-of-the-art BO without prior knowledge, outperforms LLM-based baselines, and uses natural-language priors to improve beyond standard BO. We further demonstrate the practical value of agentic BO in dynamic settings, where Sara reconfigures the full optimization problem on the fly as requirements change, a capability not previously available in standard BO.

Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, yet many real-world optimization problems contain substantially richer information than function evaluations alone. Examples include training curves in hyperparameter optimization, expert notes and images in scientific experimentation, and prior knowledge about where optima may lie. We show that large language models (LLMs) can effectively leverage such rich auxiliary information to guide optimization. Motivated by these findings, we develop three methods for incorporating auxiliary information into BO using LLMs. Across hyperparameter optimization benchmarks and a real-world nuclear fusion optimization task, our methods consistently outperform both standard BO and existing LLM-based optimization approaches. Our results demonstrate the effectiveness of LLMs for leveraging rich auxiliary information in BO.

As LLMs evolve from code completion systems into autonomous scientific agents, evaluating their ability to conduct experiments has become increasingly important. Existing benchmarks typically focus on static code generation, paper replication, or final answer correctness, but do not directly assess whether agents can interpret experimental evidence and use it to guide subsequent hyperparameter decisions. To address this gap, we introduce AgentHPOBench, a sequential benchmark comprising 30 executable machine learning tasks across seven research categories. Each task begins with a validated baseline run, after which an agent performs several sequential interventions. At each step, the agent observes the accumulated configurations, metrics, and logs before proposing the next valid configuration. We evaluate 12 widely used agents and conventional HPO baselines under a unified protocol. The results show that current agents exhibit measurable experimental optimization ability across domains, but still face clear limitations in sustained iterative refinement, complex log diagnosis, and consistent progress toward reported reference performance.