Distributed dynamic online learning with differential privacy via path-length measurement

Abstract

Dynamic online learning has been given great concerns as real-time and non-stationary systems develop and it can be used for solving many practical sequential decision problems like dynamic recommendation systems for online advertisement. Due to the large volume of big data in online learning, dynamic online learning is required to be deployed under the distributed framework where the communication among agents is time-varying and real-time. Meanwhile, since the information sharing among agents is vulnerable to interception by the adversary, the privacy protection problem is significant, but to the best of our knowledge, this work is the first to consider privacy-preserving distributed online learning under dynamic circumstances. Specifically, based on a differentially private distributed online gradient descent algorithm, we minimize the regret of the network. Moreover, via the rigorous mathematical analysis, we achieve the sublinear regret bound under ϵ-differential privacy, that is, we respectively obtain O(T+VT) and O(log⁡T+VT) for convex and strongly convex function, where T is the time horizon and the path-length VT reflects the variation of the minimizer sequence. The experiments performed on the real datasets validate that the presented algorithm achieves acceptable optimization performance even when privacy protection is relatively strict.