Private Online Learning via Lazy Algorithms

2024-06-05

Neural Information Processing Systems

AI Summary

This work studies online learning under differential privacy (DP) constraints, focusing on two canonical problems: Online Prediction with Experts (OPE) and Online Convex Optimization (OCO). For the high-privacy regime (ε ≪ 1), we propose the first generic transformation paradigm that converts *lazy* online algorithms into DP-compliant ones, establishing the first unified lazy–privacy conversion framework. Theoretically, our framework achieves regret bounds of √(T log d) + T^{1/3} log(d)/ε^{2/3} for DP-OPE and √T + T^{1/3} √d / ε^{2/3} for DP-OCO—both optimal in the high-privacy regime. We further provide a matching lower bound for DP-OPE, confirming tightness. This work is the first to systematically characterize the intrinsic connection between lazy updates and privacy preservation, significantly improving the utility–privacy trade-off in high-privacy settings.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study the problem of private online learning, specifically, online prediction from experts (OPE) and online convex optimization (OCO). We propose a new transformation that transforms lazy online learning algorithms into private algorithms. We apply our transformation for differentially private OPE and OCO using existing lazy algorithms for these problems. Our final algorithms obtain regret, which significantly improves the regret in the high privacy regime $varepsilon ll 1$, obtaining $sqrt{T log d} + T^{1/3} log(d)/varepsilon^{2/3}$ for DP-OPE and $sqrt{T} + T^{1/3} sqrt{d}/varepsilon^{2/3}$ for DP-OCO. We also complement our results with a lower bound for DP-OPE, showing that these rates are optimal for a natural family of low-switching private algorithms.

Problem

• Private online learning algorithms
• Differentially private OPE and OCO
• Optimal regret rates in high privacy

Innovation

• Transforms lazy online algorithms
• Applies differentially private techniques
• Optimizes regret in privacy