Multi-Agent LLMs for Adaptive Acquisition in Bayesian Optimization

Bayesian Optimization (BO) is widely used to optimize expensive black-box objectives by learning a probabilistic surrogate and querying new points via an acquisition function. Classic approaches, however, tightly bind acquisition behavior to the surrogate (often a GP) and a small set of fixed statistics, which can make exploration–exploitation tradeoffs inflexible and sensitive to hyperparameters. These limitations become acute in higher-dimensional or irregular landscapes relevant to engineering design. We propose an agentic LLM framework that shifts the locus of intelligence from a static, model-tied acquisition rule to a problem-adaptive acquisition designer implemented with one or more large language models. Prior LLM-for-optimization efforts have largely focused on direct candidate generation (or meta-prompted solution search), leaving the acquisition design step to conventional surrogates; by contrast, we use LLM agents to recommend task-appropriate metrics and weights and to compose an acquisition function aligned with user criteria. This fills a gap identified in the literature, addressing prompt rigidity and the lack of user-aligned selection criteria in existing frameworks. We instantiate two protocols. In the single-agent setting, a structured prompt provides the problem description history of evaluated points, and a library of metric definitions; the agent then: 1. selects the metrics and weights, 2. constructs the acquisition, and 3. proposes the next candidate. In the multi-agent setting, the task is decomposed into two coordinated prompts: Agent A outputs only the metric–weight set; Agent B consumes that set to produce the acquisition and a single candidate. This division reduces prompt overload and makes the designer more modular and auditable. Across both protocols, the metrics library focuses on four complementary desiderata for BO sampling: exploration, exploitation, representativeness, and diversity. These criteria bias acquisition design toward balanced early-stage coverage and sustained local refinement, and they are explicitly surfaced to the agent(s) to support transparent tradeoff reasoning. Experimental Design. We evaluate on three representative problems: 1. the Rosenbrock function (smooth with a narrow, curved valley), 2. hyperparameter tuning (costly evaluations; test accuracy as objective), and 3. robot pushing (discontinuous dynamics; positioning error objective). For each task, we run both single and multi-agent protocols. All experiments utilize the LLAMA3.3 model, locally hosted on UIC servers, ensuring reproducibility without third-party API dependencies. Results & Analysis. We analyze performance using the four explicit criteria above, enabling like-for-like comparisons of sampling behavior and search quality, especially in the early budget, where BO decisions are most consequential. The study reports results for each task under both protocols, highlighting how metric selection influences acquisition design and, in turn, sampling trajectories. Contributions. 1. A problem-adaptive acquisition designer using single and multi-agent LLM protocols, moving beyond candidate-only LLM sampling; 2. a transparent metrics-and-weights interface for user-aligned acquisition construction; 3. a general prompting schema that separates metric selection from acquisition and candidate generation to improve modularity and auditability; 4. an evaluation suite spanning smooth, costly, and discontinuous landscapes, with locally hosted infrastructure for reproducibility.