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The goal of active learning is to achieve the same accuracy achievable by passive learning, while using much fewer labels. Exponential savings in terms of label complexity have been proved in very special cases, but fundamental lower bounds show that such improvements are impossible in general. This suggests a need to explore alternative goals for active learning. Learning with abstention is one such alternative. In this setting, the active learning algorithm may abstain from prediction and incur an error that is marginally smaller than random guessing. We develop the first computationally efficient active learning algorithm with abstention. Our algorithm provably achieves p o l y l o g ( 1 ε ) label complexity, without any low noise conditions. Such performance guarantee reduces the label complexity by an exponential factor, relative to passive learning and active learning that is not allowed to abstain. Furthermore, our algorithm is guaranteed to only abstain on hard examples (where the true label distribution is close to a fair coin), a novel property we term \emph{proper abstention} that also leads to a host of other desirable characteristics (e.g., recovering minimax guarantees in the standard setting, and avoiding the undesirable noise-seeking'' behavior often seen in active learning). We also provide novel extensions of our algorithm that achieve \emph{constant} label complexity and deal with model misspecification.
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Active Learning with Neural Networks: Insights from Nonparametric Statistics
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 label complexity, without any low noise assumptions. We also provide extensions of our results beyond the commonly studied Sobolev/H\"older spaces and develop label complexity guarantees for learning in Radon spaces, which have recently been proposed as natural function spaces associated with neural networks.
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- Award ID(s):
- 2023239
- PAR ID:
- 10533133
- Publisher / Repository:
- Advances in Neural Information Processing Systems
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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