An Information-Theoretic Framework for Unifying Active Learning Problems
This work provides a unified theoretical framework and practical algorithms for researchers and practitioners working on active learning, particularly in level set estimation and Bayesian optimization, offering performance improvements and new insights into existing methods.
This paper introduces an information-theoretic framework that unifies active learning problems such as level set estimation (LSE) and Bayesian optimization (BO). The framework yields a new active learning criterion that achieves state-of-the-art performance in continuous-input LSE problems and a competitive acquisition function for BO, while also revealing a drawback in max-value entropy search (MES).
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.