Context-Aware Kernel Search for Bayesian Optimization with Large Language Models
Keywords: Bayesian optimization, Gaussian processes, kernel design, large language models
TL;DR: We introduce Context-Aware Kernel Search (CAKES), a novel method that automates kernel design in Bayesian optimization using large language models.
Abstract: The efficiency of Bayesian optimization (BO) relies on careful selection of the surrogate model to balance exploration and exploitation under limited budget. Traditional BO methods often struggle with sub-optimal kernel choices when using Gaussian processes (GPs) as the surrogate model. When the kernel is inadequately chosen, BO may converge slowly or even get stuck at an undesired local minimum. To address such drawback, we propose the novel Context-Aware Kernel Search (CAKES) to automate optimal kernel design in BO with large language models (LLMs). Concretely, CAKES exploits LLMs as crossover and mutation operators to adaptively generate and refine GP kernels based on the observed data. CAKES works entirely in-context and can be easily integrated into existing systems without requiring any fine-tuning. We further present a theoretical analysis demonstrating that our method achieves sub-linear regret relative to the budget for any input dimension. Experimental results demonstrate that CAKES outperforms various salient baseline methods in numerous synthetic and real-world optimization tasks. Notably, CAKES improves the overall performance on benchmark functions by roughly 36\%. In hyperparameter tuning tasks, CAKES can effectively leverage fewer data samples to quickly identify high-performing configurations and consistently ranks first across various datasets. As an encouraging real application, we successfully applied CAKES to design photonic chips, achieving significant improvements in key performance indicators while speeding up the design cycle by a factor of ten compared to the baselines. Our code is accessible at https://github.com/cakes4bo/cakes.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 5709
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