Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function. To ensure the quality of the model, transfer learning approaches have been developed to automatically design GP priors by learning from observations on "training" functions. These training functions are typically required to have the same domain as the "test" function (black-box function to be optimized). In this paper, we introduce MPHD, a model pre-training method on heterogeneous domains, which uses a neural net mapping from domain-specific contexts to specifications of hierarchical GPs. MPHD can be seamlessly integrated with BO to transfer knowledge across heterogeneous search spaces. Our theoretical and empirical results demonstrate the validity of MPHD and its superior performance on challenging black-box function optimization tasks.

翻译：贝叶斯优化（BO）是一种流行的黑箱函数优化方法，它基于函数的贝叶斯模型（通常为高斯过程（GP））进行序贯决策。为确保模型质量，研究人员开发了迁移学习方法，通过从“训练”函数的观测中自动设计GP先验。这些训练函数通常需要与待优化的“测试”函数（黑箱函数）具有相同的定义域。本文提出了一种异构域上的模型预训练方法MPHD，该方法利用神经网络将特定域上下文映射至分层GP的规范。MPHD可无缝集成至BO中，实现跨异构搜索空间的知识迁移。我们的理论与实证结果表明了MPHD的有效性及其在挑战性黑箱函数优化任务中的优越性能。