Active learning provides a framework to adaptively query the most informative experiments towards learning an unknown black-box function. Various approaches of active learning have been proposed in the literature, however, they either focus on exploration or exploitation in the design space. Methods that do consider exploration-exploitation simultaneously employ fixed or ad-hoc measures to control the trade-off that may not be optimal. In this paper, we develop a Bayesian hierarchical approach, referred as BHEEM, to dynamically balance the exploration-exploitation trade-off as more data points are queried. To sample from the posterior distribution of the trade-off parameter, We subsequently formulate an approximate Bayesian computation approach based on the linear dependence of queried data in the feature space. Simulated and real-world examples show the proposed approach achieves at least 21% and 11% average improvement when compared to pure exploration and exploitation strategies respectively. More importantly, we note that by optimally balancing the trade-off between exploration and exploitation, BHEEM performs better or at least as well as either pure exploration or pure exploitation.

翻译：主动学习提供了一种自适应查询最具信息量的实验以学习未知黑箱函数的框架。文献中已提出多种主动学习方法，但这些方法要么仅关注设计空间的探索，要么仅关注利用。那些同时考虑探索-利用的方法采用固定或启发式措施控制权衡，这可能并非最优。本文提出了一种名为BHEEM的贝叶斯层次方法，随着数据点的逐步查询，动态平衡探索-利用权衡。为了对权衡参数的后验分布进行抽样，我们随后基于查询数据在特征空间中的线性依赖性，构建了一种近似贝叶斯计算方法。仿真与真实案例表明，与纯探索和纯利用策略相比，所提方法分别实现了至少21%和11%的平均性能提升。更重要的是，我们注意到，通过最优平衡探索与利用之间的权衡，BHEEM的性能优于或至少不逊于纯探索或纯利用策略。