The Design And Analysis Of Asynchronous Gossip Algorithm For Stochastic Optimization With Approximate Projections

Recently,the rapid development of distributed optimization technology has attracted more and more attention from scholars at home and abroad.Distributed optimization technology is used in various industry fields.Common applications include path planning,resource allocation,traffic control,and so on.In this article,we are going to study the real-time measurement and monitoring of information in the wireless sensor network by using various sensors in the network,and the data obtained by each sensor interacts with the surrounding sensors to realize the sharing and fusion between the data.The wireless sensor network in this paper can be regarded as a multi-agent network system,and each sensor of the wireless sensor system can be regarded as an agent.Each sensor carries a cost function for the entire wireless sensor network.The objective function is the sum of the cost functions of the individual sensors.In the process of iterating the agent in the sensor network,we find that the objective function of the sensor is not smooth,in other words,it is not microscopic.At this time,the state value cannot be calculated by the traditional gradient method.Therefore,we adopted subgradient method.In addition,we find that it is very cumbersome to calculate the sub-gradient of a cost function.Therefore,in order to reduce the number of iterations of the agent,we introduce an approximate projection algorithm,so that the computational complexity of the algorithm will be greatly reduced.The specific work arrangements are as follows:1.The first consideration is that the connection between all individuals in the wireless sensor network is fixed,that is,in the case of a fixed topology,At this time,the weight matrix in the iterative formula is set to be invariant.We analyze the consistency and convergence of the asynchronous distributed projection algorithm and give relevant conclusions to prove the feasibility of the algorithm.2.Considering that the connection between all individuals in the wireless sensor network is variable,that is,in the case of a time-varying topology.At this moment,the iterative formula of the agent in the system will change,and the weight matrix will also change.Taking this into account,we use the asynchronous time distributed approximate projection algorithm to analyze the consistency and convergence,and verify the feasibility of the algorithm.3.Based on the previous foundation,we will consider a more general case,that is,the information transmitted between the agents is quantitative information.At this point,we will design a specific uniform quantizer,and integrate the quantizer into the asynchronous time distributed approximate projection algorithm,and then analyze the consistency and convergence of the algorithm again,and analyze the factors affecting the convergence of the algorithm.In the future work,we can further study the approximate projection algorithm of asynchronous stepsize.This stepsize is related to the number of iterations of the algorithm,which is closer to the actual situation and worthy of further study.