Active learning provides a framework to adaptively sample 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 to dynamically balance the exploration-exploitation trade-off as more data points are queried. We subsequently formulate an approximate Bayesian computation approach based on the linear dependence of data samples in the feature space to sample from the posterior distribution of the trade-off parameter obtained from the Bayesian hierarchical model. Simulated and real-world examples show the proposed approach achieves at least 6% 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, our approach 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框架，用于自适应地采样最具信息量的实验，以学习未知的黑箱函数。文献中已提出多种主动学习方法，然而它们要么侧重于设计空间中的探索，要么侧重于利用。那些同时考虑探索-利用的方法采用固定的或启发式的措施来控制权衡，这可能并非最优。本文开发了一种贝叶斯层次方法，随着更多数据点的查询，动态平衡探索-利用的权衡。随后，我们基于特征空间中数据样本的线性依赖性，构建了一种近似贝叶斯计算方法，用于从贝叶斯层次模型获得的权衡参数后验分布中进行采样。模拟和真实世界示例表明，与纯探索和纯利用策略相比，所提方法平均分别实现了至少6%和11%的提升。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，我们的方法表现优于或至少不逊于纯探索或纯利用策略。