Agentic-MatriBO: Capability-Compiled Agentic Bayesian Optimization for Materials and Chemical Design

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.

Black-box optimization (BBO) arises in many scientific and engineering problems where objective evaluations are expensive and limited. Recent large language model (LLM) agents offer a new way to approach BBO by combining task semantics, computation, optimization tools, and feedback-driven decision making, showing great potential due to the integration with mathematically rigorous tools. However, existing agentic BBO studies use different task domains and system configurations, making their results difficult to compare and the effects of individual design choices hard to isolate. We therefore introduce AgenticBBO-Bench, a cross-domain benchmark for agentic BBO spanning synthetic functions, hyperparameter optimization, database tuning, chip design, and molecular design under a unified finite-budget evaluation protocol. In our experiments, agentic BBO achieves higher family-averaged scores than direct LLM-based methods in all five domains and outperforms the best numerical optimizers in four. We further study three factors shaping agent performance: optimization tools, task information and prior knowledge, and the role of the LLM during search. Our results show that additional numerical tools do not consistently improve performance, task semantics are broadly useful while more specific priors are less reliable, and numerical optimizers can effectively absorb gains from search trajectories established by the agent. Finally, we introduce a five-task frontier challenge within AgenticBBO-Bench and evaluate seven LLMs under the Codex agent harness, where GPT-6 Astra and DeepSeek-V4.1-Flash lie on the Pareto frontier of performance and cost among the evaluated models. Our code is available at https://github.com/lamda-bbo/agentic-bbo.

Mixed-variable optimization in scientific discovery often requires exploring large combinatorial spaces under costly experimental evaluations, making sample?efficient Bayesian optimization (BO) essential. However, existing BO methods typ?ically rely on structural descriptors to define similarity among categorical variables, implicitly assuming that structural similarity reflects similarity in task performance. In scientific optimization, this assumption is often violated, leading to surrogate representations that are poorly aligned with the optimization objective. To address this limitation, we propose TagBO (Task-aware Graph Bayesian Optimization), a method that integrates LLM-derived relational priors with descriptor-based struc?tural information for mixed-variable Bayesian optimization. Rather than directly using LLM outputs as predictive scores, TagBO treats LLM outputs as a potentially noisy source of task-aware relational priors and extracts coarse ordinal relational signals from LLM reasoning to construct task-aware similarity structures for scien?tific optimization. TagBO then performs constrained Gaussian process Bayesian optimization over the resulting joint discrete-continuous representation space. Ex?periments on diverse chemistry and materials formulation tasks demonstrate that TagBO consistently improves sample efficiency under fixed evaluation budgets across LLMs of varying capabilities.