A fundamental issue in active learning of Gaussian processes is that of the exploration-exploitation trade-off. This paper presents a novel nonmyopic (∈)-Bayes-optimal active learning ((∈)-BAL) approach that jointly optimizes the trade-off. In contrast, existing works have primarily developed greedy algorithms or performed exploration and exploitation separately. To perform active learning in real time, we then propose an anytime algorithm based on (∈)-BAL with performance guarantee and empirically demonstrate using a real-world dataset that, with limited budget, it outperforms the state-of-the-art algorithms.
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