Both Bayesian optimization and active learning realize an adaptive sampling scheme to achieve a specific learning goal. However, while the two fields have seen an exponential growth in popularity in the past decade, their dualism has received relatively little attention. In this paper, we argue for an original unified perspective of Bayesian optimization and active learning based on the synergy between the principles driving the sampling policies. This symbiotic relationship is demonstrated through the substantial analogy between the infill criteria of Bayesian optimization and the learning criteria in active learning, and is formalized for the case of single information source and when multiple sources at different levels of fidelity are available. We further investigate the capabilities of each infill criteria both individually and in combination on a variety of analytical benchmark problems, to highlight benefits and limitations over mathematical properties that characterize real-world applications.

翻译：贝叶斯优化与主动学习均通过自适应采样策略实现特定的学习目标。尽管这两个领域在过去十年中呈现出指数级增长，但两者之间的二元性却鲜少受到关注。本文基于驱动采样策略原理间的协同作用，提出贝叶斯优化与主动学习的原创性统一视角。这种共生关系通过贝叶斯优化的填充准则与主动学习中的学习准则之间的实质性类比得以证明，并在单一信息源及存在不同保真度多源信息的场景下进行了形式化建模。我们进一步在多种分析基准问题上分别探究各填充准则的独立与组合性能，以揭示其在表征真实应用的数学特性上的优势与局限性。