Active Learning with Neural Networks: Insights from Nonparametric Statistics
This work addresses a significant theory-practice gap in deep active learning, offering theoretical insights that could benefit researchers and practitioners aiming to reduce labeled data requirements in machine learning.
The paper tackles the lack of rigorous label complexity guarantees for deep active learning by providing the first near-optimal guarantees, showing that active learning with neural networks can achieve minimax label complexity under low noise conditions and polylog(1/ε) complexity with an abstention option.
Deep neural networks have great representation power, but typically require large numbers of training examples. This motivates deep active learning methods that can significantly reduce the amount of labeled training data. Empirical successes of deep active learning have been recently reported in the literature, however, rigorous label complexity guarantees of deep active learning have remained elusive. This constitutes a significant gap between theory and practice. This paper tackles this gap by providing the first near-optimal label complexity guarantees for deep active learning. The key insight is to study deep active learning from the nonparametric classification perspective. Under standard low noise conditions, we show that active learning with neural networks can provably achieve the minimax label complexity, up to disagreement coefficient and other logarithmic terms. When equipped with an abstention option, we further develop an efficient deep active learning algorithm that achieves $\mathsf{polylog}(\frac{1}ε)$ label complexity, without any low noise assumptions. We also provide extensions of our results beyond the commonly studied Sobolev/Hölder spaces and develop label complexity guarantees for learning in Radon $\mathsf{BV}^2$ spaces, which have recently been proposed as natural function spaces associated with neural networks.