Research On Distributed Online Optimization Algorithm With Privacy Protection

With the advent of the era of big data,distributed optimization has been widely used to deal with massive data.Among them,distributed recursive least square algorithm and distributed algorithm without projection are commonly used.We propose an online algorithm based on Gaussian mechanism and resetting sub-gradient technique,which can not only solve the problem of differential optimization on a directed graph with row random matrix under distributed constraints,but also maintain and maintain a certain degree of differential privacy.Despite the success of these algorithms,the projection operations they require still limit their further applicability in many environments of practical interest.In order to solve the disadvantages of this technology,a distributed algorithm without projection is proposed.The main work of this paper is divided into two modules.In the first module,a non-projection distributed online conditional gradient optimization problem with differential privacy is proposed based on the non-projection distributed algorithm.To address this problem,a distributed online conditional gradient(D-OCG)algorithm is proposed as an expected variant,which avoids projection operations by using a linear minimization step.The network model for this problem is a balanced undirected graph with five nodes.We know from the rational demonstration that the expected regret bound of this algorithm for general convex local loss function is,where is the time range.This result and regret analysis can realize the requirement of privacy protection.Finally,the simulation results show the effectiveness of the proposed algorithm.In the second module,based on the unbalanced directed network,a distributed constraint online optimization method with privacy protection is proposed.Projection gradient algorithm is also used in the proposed distributed constrained online optimization method,in which each agent in line with the random matrix adjacent agents and imbalance on the directed graph of the exchange of local information,in this case,the process of information transmission is easy to cause information leakage,to protect the privacy of data,this paper proposes a online distributed constraint optimization method with privacy protection.Under appropriate assumptions,a dynamic regret bound is established for each agent,which increases sub-linearly as long as the growth rate of the minimum sequence deviation is within a certain range.Finally,a simulation example is given to verify the effectiveness of the proposed method.Figure[11]table[2]reference[55]...