Harnessing Large Language Models to Compile Task-Relevant Context into Bayesian Optimisation

Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, yet it typically reduces each expensive experiment to an input and its objective value, discarding much of the information the experiment produces. Such auxiliary information can include training curves in hyperparameter optimization, expert notes and images in scientific experimentation, or known facts about the specific optimization problem. Leveraging the ability of large language models (LLMs) to process diverse and unstructured information, we introduce two methods: AuxBO-Evolve, which uses auxiliary information to evolve beliefs over the location of the optimum, and AuxBO-Vicinity, which uses it to locally guide the acquisition function. Across synthetic tasks, hyperparameter optimization benchmarks, and a nuclear fusion task with unstructured scientist-written logs, our methods consistently improve optimization performance and outperform standard BO and existing LLM-based approaches. We further find that LLMs provide more effective probabilistic guidance when modeling likely maximizer locations rather than objective values pointwise. Overall, our results demonstrate that exploiting rich information beyond standard $(\mathbf{x}, y)$ interactions can substantially improve BO performance.

Large language model (LLM)-guided Bayesian optimization (BO) uses past observations to guide search, but proposed directions and their revision can remain implicit. We propose Feedback-Guided Search State (FGSS), a structured hypothesis-management interface connecting language-based guidance to observed evidence, executable parameter interventions, and comparative support updates. An LLM reflector proposes and revises hypotheses; a deterministic curator validates them and maintains identities and test records. The evolving state guides candidate construction and priorities. Instantiated on LLAMBO, FGSS-BO retains its surrogate and default expected improvement selection, with a bounded testing policy. On two retrospective protocol/media tasks with nearest-neighbor response oracles, it attains higher sample mean final best and search AUC than the matched LLAMBO baseline and evaluated non-LLM baselines. Prose-reflection and EI-only controls show mixed component effects. Six direct-training hyperparameter-optimization tasks show task-dependent transfer, strongest on diabetes SVM; exact-grid and reaction controls examine other settings. FGSS exposes hypotheses, their execution, and cross-round revisions for inspection while supporting search gains in selected settings.

Optimization of LLM training and inference configurations, such as hyperparameters, data mixtures, and prompts, is critical to performance, but it is often approached heuristically in practice, leading to potentially suboptimal outcomes. By framing them as noisy, expensive, and derivative-free optimization problems, Bayesian optimization (BO) and other black-box optimization (BBO) methods offer a promising yet underexplored direction for principled, sample-efficient methods. However, LLM training and inference costs are prohibitively high for most of the BBO research community, and new methods are often only evaluated on synthetic test functions and small-scale datasets that fail to capture the challenges of modern LLM optimization problems. This impedes the development of BBO methods and makes it difficult to assess their effectiveness on modern LLM tasks. We introduce BoLT, the first LLM-centric benchmark that democratizes LLM research for the BBO community. BoLT is released at https://github.com/chewwt/bolt. BoLT covers broad and well-motivated LLM optimization problems, involving multi-fidelity, multi-objective, heteroscedastic noise, and high-dimensional search spaces. Each problem in BoLT is grounded in real experimental data and made fully reproducible and accessible through lightweight surrogate models fitted to the results of thousands of real LLM experiments. We benchmark BoLT against an extensive range of BO and BBO methods, showing that selected BO methods consistently outperform others across tasks and highlighting gaps in existing BBO methods on LLM tasks, underscoring the need to modernize benchmarks for the BBO community.