Differentially Private Distributed Online Algorithms over Time-Varying Directed Networks

We consider a private distributed online optimization problem where a set of agents aim to minimize the sum of locally convex cost functions while each desires that the local cost function of individual agent is kept differentially private. To solve such problem, we propose differentially private distributed stochastic subgradient online optimization algorithm over time-varying directed networks. We use differential privacy to preserve the privacy of participating agents. We show that our algorithm preserves differential privacy and achieves logarithmic expected regret under locally strong convexity. Moreover, we also show that square-root expected regret is obtained under local convexity. Furthermore, we reveal the tradeoff between the privacy level and the performance of our algorithm.