  In this paper, we study a distributed privacy-preserving learning problem in
social networks with general topology. The agents can communicate with each
other over the network, which may result in privacy disclosure, since the
trustworthiness of the agents cannot be guaranteed. Given a set of options
which yield unknown stochastic rewards, each agent is required to learn the
best one, aiming at maximizing the resulting expected average cumulative
reward. To serve the above goal, we propose a four-staged distributed algorithm
which efficiently exploits the collaboration among the agents while preserving
the local privacy for each of them. In particular, our algorithm proceeds
iteratively, and in every round, each agent i) randomly perturbs its adoption
for the privacy-preserving purpose, ii) disseminates the perturbed adoption
over the social network in a nearly uniform manner through random walking, iii)
selects an option by referring to the perturbed suggestions received from its
peers, and iv) decides whether or not to adopt the selected option as
preference according to its latest reward feedback. Through solid theoretical
analysis, we quantify the trade-off among the number of agents (or
communication overhead), privacy preserving and learning utility. We also
perform extensive simulations to verify the efficacy of our proposed social
learning algorithm.
