Differentially Private Online Learning

In this paper, we consider the problem of preserving privacy in the online learning setting. Online learning involves learning from the data in real-time, so that the learned model as well as its outputs are also continuously changing. This makes preserving privacy of each data point significantly more challenging as its effect on the learned model can be easily tracked by changes in the subsequent outputs. Furthermore, with more and more online systems (e.g. search engines like Bing, Google etc.) trying to learn their customer’s behavior by leveraging their access to sensitive customer data (through cookies etc), the problem of privacy preserving online learning has become critical as well. We study the problem in the online convex programming (OCP) framework—a popular online learning setting with several interesting theoretical and practical implications—while using differential privacy as the formal privacy measure. For this problem, we distill two critical attributes that a private OCP algorithm should have in order to provide reasonable privacy as well as utility guarantees: 1) linearly decreasing sensitivity, i.e., as new data points arrive their effect on the learning model decreases, 2) sub-linear regret bound—regret bound is a popular goodness/utility measure of an online learning algorithm. Given an OCP algorithm that satisfies these two conditions, we provide a general framework to convert the given algorithm into a privacy preserving OCP algorithm with good (sub-linear) regret. We then illustrate our approach by converting two popular online learning algorithms into their differentially private variants while guaranteeing sub-linear regret (O( √ T )). Next, we consider the special case of online linear regression problems, a practically important class of online learning problems, for which we generalize an approach by [13] to provide a differentially private algorithm with just O(log T ) regret. Finally, we show that our online learning framework can be used to provide differentially private algorithms for offline learning as well. For the offline learning problem, our approach obtains better error bounds as well as can handle larger class of problems than the existing state-of-the-art methods [3].