Unlabeled Data Help: Minimax Analysis and Adversarial Robustness

TL;DR

This paper provides a minimax analysis of reconstruction-based self-supervised learning, demonstrating its rate-optimality under various models and showing that unlabeled data can enhance adversarial robustness.

Contribution

It offers the first rigorous minimax analysis for reconstruction-based SSL and integrates it with adversarial training to improve robustness.

Findings

Reconstruction-based SSL is rate-optimal under certain models.

Unlabeled data improves adversarial robustness.

Theoretical validation of SSL's effectiveness with unlabeled data.

Abstract

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.