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 position 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学习目标。然而，尽管这两个领域在过去十年间呈指数级增长，其二元共生关系却鲜受关注。本文作为立场论文，基于驱动采样策略原则间的协同效应，提出贝叶斯优化与主动学习的原创性统一视角。通过论证贝叶斯优化填充准则与主动学习准则之间的本质对偶性，我们阐释了这种共生关系，并针对单一信息源以及多保真度多信息源场景进行了形式化建模。进一步地，我们系统评估了各类填充准则在多种解析基准问题中的独立及组合性能，揭示其针对实际应用数学特征的优劣特性。