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arXiv · 2012.10695

An Information-Theoretic Framework for Unifying Active Learning Problems

Quoc Phong Nguyen·Bryan Kian Hsiang Low·Patrick Jaillet
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Abstract

This paper presents an information-theoretic framework for unifying active learning problems: level set estimation (LSE), Bayesian optimization (BO), and their generalized variant. We first introduce a novel active learning criterion that subsumes an existing LSE algorithm and achieves state-of-the-art performance in LSE problems with a continuous input domain. Then, by exploiting the relationship between LSE and BO, we design a competitive information-theoretic acquisition function for BO that has interesting connections to upper confidence bound and max-value entropy search (MES). The latter connection reveals a drawback of MES which has important implications on not only MES but also on other MES-based acquisition functions. Finally, our unifying information-theoretic framework can be applied to solve a generalized problem of LSE and BO involving multiple level sets in a data-efficient manner. We empirically evaluate the performance of our proposed algorithms using synthetic benchmark functions, a real-world dataset, and in hyperparameter tuning of machine learning models.

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Quoc Phong Nguyen, Bryan Kian Hsiang Low, Patrick Jaillet. 2020-12-19. An Information-Theoretic Framework for Unifying Active Learning Problems. https://arxiv.org/abs/2012.10695

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