Private Learning Implies Online Learning: An Efficient Reduction

TL;DR

This paper establishes an efficient black-box reduction from differentially private learning to online learning, resolving an open question about the implications of privacy-preserving algorithms in online settings.

Contribution

It provides the first efficient reduction showing that differentially private learning implies online learning from expert advice.

Findings

Efficient reduction from private learning to online learning.

Addresses an open problem in the theory of private and online learning.

Clarifies the relationship between privacy and online learning efficiency.

Abstract

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online learning from expert advice.