Unlabeled Data Help: Minimax Analysis and Adversarial Robustness
This work addresses the theoretical understanding and practical enhancement of self-supervised learning for improving adversarial robustness in machine learning, though it is incremental as it builds on existing algorithms.
The paper provides a rigorous minimax analysis to justify the rate-optimality of a reconstruction-based self-supervised learning algorithm under various statistical models, showing it fully utilizes labeled and unlabeled data, and demonstrates that incorporating this algorithm into adversarial training improves robustness.
The recent proposed self-supervised learning (SSL) approaches successfully demonstrate the great potential of supplementing learning algorithms with additional unlabeled data. However, it is still unclear whether the existing SSL algorithms can fully utilize the information of both labelled and unlabeled data. This paper gives an affirmative answer for the reconstruction-based SSL algorithm \citep{lee2020predicting} under several statistical models. While existing literature only focuses on establishing the upper bound of the convergence rate, we provide a rigorous minimax analysis, and successfully justify the rate-optimality of the reconstruction-based SSL algorithm under different data generation models. Furthermore, we incorporate the reconstruction-based SSL into the existing adversarial training algorithms and show that learning from unlabeled data helps improve the robustness.