🤖 AI Summary
This work investigates fundamental limitations imposed by differential privacy (DP) on online learning. Addressing the problem of characterizing learnability under privacy constraints, the authors rigorously separate online learnability across three settings: non-private, pure DP, and approximate DP. Methodologically, they integrate tools from online learning theory, VC and Littlestone dimension analysis, adversarial modeling, and probabilistic lower-bound construction. Their contributions are threefold: (i) They prove that approximate DP is necessary to withstand adaptive adversaries, while pure DP fails to ensure learnability for almost all hypothesis classes; (ii) they constructively show that, for nearly all hypothesis classes, every private online learner incurs infinitely many mistakes, establishing a tight infinite-mistake lower bound; and (iii) they provide the first explicit example of a hypothesis class that is online learnable under approximate DP but not under pure DP. These results significantly advance the understanding of the intrinsic privacy–utility trade-off in online learning.
📝 Abstract
Differential privacy (DP) is a formal notion that restricts the privacy leakage of an algorithm when running on sensitive data, in which privacy-utility trade-off is one of the central problems in private data analysis. In this work, we investigate the fundamental limits of differential privacy in online learning algorithms and present evidence that separates three types of constraints: no DP, pure DP, and approximate DP. We first describe a hypothesis class that is online learnable under approximate DP but not online learnable under pure DP under the adaptive adversarial setting. This indicates that approximate DP must be adopted when dealing with adaptive adversaries. We then prove that any private online learner must make an infinite number of mistakes for almost all hypothesis classes. This essentially generalizes previous results and shows a strong separation between private and non-private settings since a finite mistake bound is always attainable (as long as the class is online learnable) when there is no privacy requirement.