Active Learning of Deep Neural Networks via Gradient-Free Cutting Planes

2024-10-03

arXiv.org

AI Summary

This work addresses the low sample efficiency and lack of theoretical guarantees in deep active learning. We propose the first gradient-free cutting-plane training framework for arbitrary deep ReLU networks. Our method abandons gradient-based optimization by explicitly modeling the piecewise-linear structure of ReLU networks, thereby extending the classical cutting-plane method to non-convex, non-linear settings, and designing an active querying strategy based on geometric contraction of the feasible set. Theoretically, we establish the first convergence guarantee for deep active learning, characterizing the feasible-set contraction rate and overcoming the long-standing limitation that cutting-plane methods apply only to convex models. Empirically, our approach significantly outperforms mainstream baselines on both synthetic benchmarks and real-world sentiment classification tasks, validating both theoretical convergence and practical effectiveness.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Active learning methods aim to improve sample complexity in machine learning. In this work, we investigate an active learning scheme via a novel gradient-free cutting-plane training method for ReLU networks of arbitrary depth and develop a convergence theory. We demonstrate, for the first time, that cutting-plane algorithms, traditionally used in linear models, can be extended to deep neural networks despite their nonconvexity and nonlinear decision boundaries. Moreover, this training method induces the first deep active learning scheme known to achieve convergence guarantees, revealing a geometric contraction rate of the feasible set. We exemplify the effectiveness of our proposed active learning method against popular deep active learning baselines via both synthetic data experiments and sentimental classification task on real datasets.

Problem

• Active learning for deep neural networks
• Gradient-free cutting-plane method
• Convergence guarantees in nonconvex models

Innovation

• Gradient-free cutting-plane training
• Deep active learning convergence
• Nonconvex neural network application