Distributed online bandit linear regressions with differential privacy

Abstract

This paper addresses the distributed online bandit linear regression problems with privacy protection, in which the training data are spread in a multi-agent network. Each node identifies a linear predictor to fit the training data and experiences a square loss on each round. The purpose is to minimize the regret that assesses the difference of the accumulated loss between the online linear predictor and the optimal offline linear predictor. Moreover, the differential privacy strategy is adopted to prevent the adversary from inferring the parameter vector of any node. Two efficient differentially private distributed online regression algorithms are developed in the cases of one-point and two-point bandit feedback. Our analysis suggests that the developed algorithms achieve ϵ-differential privacy and establish the regret upper bounds in O(K3/4) and O(K) for one-point and two-point bandit feedback, respectively, where K is the time horizon. We also show that there exists a tradeoff between our algorithms’ privacy level and convergence. Finally, the performance of the proposed algorithms is validated by a numerical example.