Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with
  LLMs
Authors: name: Richard Cornelius Suwandi, name: Feng Yin, name: Juntao Wang, name: Renjie Li, name: Tsung-Hui Chang, name: Sergios Theodoridis

The efficiency of Bayesian optimization (BO) relies heavily on the choice of
the Gaussian process (GP) kernel, which plays a central role in balancing
exploration and exploitation under limited evaluation budgets. Traditional BO
methods often rely on fixed or heuristic kernel selection strategies, which can
result in slow convergence or suboptimal solutions when the chosen kernel is
poorly suited to the underlying objective function. To address this limitation,
we propose a freshly-baked Context-Aware Kernel Evolution (CAKE) to enhance BO
with large language models (LLMs). Concretely, CAKE leverages LLMs as the
crossover and mutation operators to adaptively generate and refine GP kernels
based on the observed data throughout the optimization process. To maximize the
power of CAKE, we further propose BIC-Acquisition Kernel Ranking (BAKER) to
select the most effective kernel through balancing the model fit measured by
the Bayesian information criterion (BIC) with the expected improvement at each
iteration of BO. Extensive experiments demonstrate that our fresh CAKE-based BO
method consistently outperforms established baselines across a range of
real-world tasks, including hyperparameter optimization, controller tuning, and
photonic chip design. Our code is publicly available at
https://github.com/cake4bo/cake.