Differential Privacy in Social Networks Using Multi-Armed Bandit

There has been an exponential growth over the years in the number of users connected to social networks. This has spurred research interest in social networks to ensure the privacy of users. From a theoretical standpoint, a social network is modeled as a directed graph network and interactions among agents in the directed graph network can be analyzed with non-Bayesian learning and online learning strategies. The goal of the agents is to learn the underlying time-varying true state of the network through repeated cooperative interaction among themselves. To overcome privacy challenges in social networks, recent research works include differential privacy in the social network analysis to guarantee the privacy of shared information among the agents. However, the common online learning strategy adopted in most existing work is the stochastic multi-armed bandit approach which assumes that the loss distribution is independent and identically distributed. This does not account for the arbitrariness of the time-varying true state in the social network. Therefore, this paper proposes a tougher but realistic setting that removes the restriction on the loss distribution. Two non-stochastic multi-armed bandit algorithms are proposed. The first algorithm uses the Laplace mechanism to guarantee differential privacy against a third-party intruder. The second algorithm uses the Laplace mechanism to guarantee differential privacy against both a third-party intruder and any spying agent in the network. The simulation results show that the agents' beliefs converge to the most dominant true state among the sequence of arbitrarily time-varying true states over the time horizon. The speed of convergence comes as a trade-off with privacy. Regret bounds are obtained for the proposed algorithms and compared to the non-private algorithm in the literature.