Dynamic Exploration-Exploitation Trade-Off in Active Learning Regression with Bayesian Hierarchical Modeling

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.