LLAMBO: LLM-Enhanced Bayesian Optimization

• LLAMBO is a framework that integrates LLMs into Bayesian optimization to improve candidate selection and enhance sample efficiency.
• It employs zero-shot warmstarting, LLM-driven surrogate modeling, and natural language-guided candidate sampling for robust optimization.
• Empirical evaluations show LLAMBO consistently lowers regret in hyperparameter tuning tasks compared to traditional methods.

The LLAMBO Framework—“LLMs to Enhance Bayesian Optimization”—is an approach that integrates LLMs into Bayesian optimization (BO) pipelines with the goal of improving sample efficiency, especially under the constraint of limited, expensive function evaluations such as those encountered in hyperparameter tuning. LLAMBO leverages the contextual understanding, encoded domain priors, and few-shot learning capabilities of LLMs to reimagine several core BO mechanisms. By framing classical BO tasks in natural language, LLAMBO enables iterative LLM-driven proposal and evaluation of candidate solutions in a modular end-to-end or component-wise fashion, without requiring LLM fine-tuning. Its effectiveness is empirically demonstrated across a broad suite of public benchmark, proprietary, and synthetic hyperparameter optimization tasks.

1. Motivation and Conceptual Foundations

The primary motivation for LLAMBO arises from recognized weaknesses in conventional BO frameworks, particularly the difficulty of building accurate surrogate models and generating high-quality candidate points when observational data are sparse or the problem is high-dimensional. These conditions are common in settings like hyperparameter optimization, where function evaluations are costly and limited in number. The LLAMBO framework addresses these limitations by exploiting the strong generalization, in-context learning, and domain transfer abilities of LLMs that have been pre-trained on massive amounts of data.

Key conceptual advantages of this integration include:

• Encoded priors allow for rapid transfer of domain knowledge with minimal data requirements.
• Few-shot learning enables the framework to generalize from a handful of observed samples.
• Natural language meta-information, including dataset and task descriptors, guides more informed exploration and exploitation.

2. Framework Structure and Mathematical Formulation

LLAMBO introduces a modular architectural shift in BO by reconceptualizing problem representation and candidate generation in natural language terms accessible to LLMs. The framework consists of three principal components:

1. Zero-shot Warmstarting: Initial candidate generation leveraging LLMs without any observed data.
2. LLM-enhanced Surrogate Modeling: Predictive modeling and uncertainty quantification using LLMs, formulated as $p(s|h;\mathcal{D}_n)$.
3. LLM-based Candidate Sampling: Generation of new candidate points conditioned on optimization objectives.

The foundational optimization problem persists in its classical form:

$h^* = \arg\min_{h} f(h)$

with the surrogate modeled as:

$$p(s|h; \mathcal{D}_n) = \int_{\Theta} p(s|h, \theta; \mathcal{D}_n) p(\theta|\mathcal{D}_n, h) d\theta$$

LLAMBO augments this setup by encoding the optimization history $\mathcal{D}_n$ as natural language sequences ($\mathcal{D}_n^{nl}$) and crafting prompts that include a problem description, dataset summary, and explicit instructions. The LLM outputs are interpreted as surrogate predictions or candidate proposals, thus blending the LLM’s reasoning with standard BO loop operations. The modularity of the system allows each component to be plugged in individually or orchestrated as a pipeline.

3. Operational Methodology and Natural Language Interface

The LLAMBO methodology reformulates each BO task step as a prompt-driven natural language task, utilizing in-context learning (ICL) for few-shot adaptation:

• Problem Serialization: The optimization task, model card (description of the ML model, hyperparameters, input/output spaces), data card (metadata), and instructions are formulated into a synthesized text prompt.
• History Encoding: Observed configuration/score pairs are serialized (e.g., "max_depth is 15, min_samples_split is 0.5, ..., accuracy is 0.9.")
• Inference and Sampling: The LLM, conditioned on prompt and history, predicts a function value (regression) and an uncertainty (obtained through repeated Monte Carlo sampling), or provides candidate configurations matching a conditional target score.

This methodology enables LLMs to contribute to both discriminative prediction (as a surrogate model) and generative proposal (candidate sampling), adapting rapidly to new optimization contexts with minimal data via ICL. Outputs can be directly used in acquisition functions or as inputs to further BO iterations.

4. Zero-shot Warmstarting Strategies

A distinctive feature of LLAMBO is its zero-shot warmstarting protocol, where LLMs suggest initial configurations before any task-specific learning. Three levels of context are investigated:

• No Context: Candidates are generated based solely on generic prompt information (no data or metadata).
• Partial Context: Prompts include dataset meta-features (sample size, feature types, etc.).
• Full Context: Prompts supplement with comprehensive distributional features, inter-feature correlations, and feature-label relationships.

Empirical evidence indicates that even absent explicit context, LLM warmstarts outperform standard random and quasirandom (e.g., Sobol) initialization, with additional context further reducing normalized regret in the initial optimization phase. Initialization points exhibit tighter correlations with true optima under full-context regimes, supplying more informative starting regions for BO.

5. Empirical Evaluation and Benchmarking

The effectiveness of LLAMBO components was rigorously evaluated:

• Benchmarks: 50 diverse tasks sampled from Bayesmark, supplemented by proprietary and synthetic datasets for hyperparameter optimization.
• Comparisons: Baseline methods included GP-DKL, SKOpt (Gaussian process), Optuna (Tree of Parzen Estimators), and SMAC3 (Random Forest).
• Outcomes: LLAMBO consistently achieved the lowest average regret, notably outperforming baselines in the early search regime (e.g., $<$10 trials), driven by stronger candidate generation and surrogate modeling.

Results further detailed the statistical properties of generated candidate sets, showing that LLAMBO’s choices—though more correlated and less diverse in some settings—explored promising regions more effectively. Both its discriminative surrogate and candidate sampler, using conditional sampling on target objectives (e.g., $s' = s_{min} - \alpha (s_{max} - s_{min})$ for exploration parameter $\alpha$), were evaluated, confirming consistent performance advantages when observations were sparse.

Component	Baseline	LLAMBO Improvement
Warmstart	Random/Sobol	Lower initial regret
Surrogate Modeling	GP, RF, TPE	Higher accuracy
Candidate Sampling	Acquisition funcs	Task-specific proposals

6. Modularity and Integration with Existing Pipelines

LLAMBO’s modular structure supports seamless integration into established BO workflows:

• Component Interoperability: Each module (warmstarting, surrogate, candidate sampler) can operate independently within or alongside other BO components.
• Adoption Scenarios: Users can employ LLAMBO for initialization only, or substitute its LLM-based surrogate within a classical BO loop, or deploy its candidate generator with external acquisition optimizers.
• Implementation: No LLM fine-tuning is required; inference is performed entirely in context. This enables rapid adoption but does incur a computational overhead due to LLM inference.

This flexibility underscores LLAMBO’s practical value: practitioners can incrementally adopt its components based on task demands, computational resources, or integration constraints.

7. Prospects and Open Challenges

Primary conclusions include:

• Accelerated Search: Zero-shot warmstarting delivers rapid initial progress.
• Enhanced Surrogate Performance: In-context LLM prediction improves exploration/exploitation decision-making.
• Flexible Control of Exploration: Target-conditioned candidate sampling offers explicit tuning of search breadth.
• Superior Sample Efficiency: Lower regrets are observed across a range of benchmarks.

Identified challenges and future research directions involve:

• Managing increased computational resources required for repeated LLM inference.
• Benchmarking performance across a wider set of LLM architectures and in higher-dimensional or more complex optimization scenarios (e.g., neural architecture search, robotic control).
• Developing bias-correction techniques, particularly for generative surrogates.

In summary, LLAMBO establishes a novel, empirically validated paradigm for fusing LLMs with Bayesian optimization, yielding demonstrable gains in sample efficiency and early-stage performance. Its flexible, modular design fosters broader applicability and invites continued research in combining LLM-driven reasoning with classical optimization frameworks.