Privacy‐preserving distributed projected one‐point bandit online optimization over directed graphs

Abstract

AbstractThe distributed online optimization (DOO) problem with privacy‐preserving properties over multiple agents is considered in this paper, where the network model is built by a strongly connected directed graph. To solve this problem, a stochastic bandit DOO algorithm based on differential privacy is proposed. This algorithm uses row‐ and column‐stochastic matrix as the weighting matrices, the requirement of the double random weighting matrix is released. To handle the unknown objective function, the one‐point bandit is used to estimate the true gradient information, and the estimated gradient information is used to update of decision variables. Different from the existing DOO algorithms that ignore privacy issues, this algorithm successfully protects the privacy of nodes through a differential privacy policy. Theoretical results show that the algorithm can not only achieve sublinear regret bounds but also protect the privacy of nodes. Finally, simulation results verify the effectiveness of the algorithm.