Design And Analysis Of Distributed Multi-agent Saddle Point Algorithm Based On Gradient-free Oracle

Nowadays,with the rise of artificial intelligence technology and the arrival of the 5G era,various high-tech industries are developing rapidly.As an important branch of the field of control disciplines,the research of distributed optimization algorithms has also attracted the attention of many scholars.With the continuous innovation and upgrading of Internet technology in the information age,distributed optimization algorithms have been continuously improved.In the face of complex realities,previous algorithms often have limitations and large computational problems.The main purpose of this paper is to improve the algorithm for various problems in the network,so that the distributed optimization problem can be effectively solved.For multi-sensor networks,this article considers each sensor as an agent.The entire wireless sensor network is a multi-agent system.In the actual problem,each agent has its own cost function,and we are committed to the minimum of all agent cost function sums to achieve the purpose of optimization.Most of the current distributed optimization methods are used to solve the convex function problem,and the function is required to be smooth,so that the optimal solution can be obtained by using the sub-gradient method.In this paper,for the convex-concave function,and the function is not smooth,the gradient-free saddle point algorithm is designed to find the optimal value.Based on the distributed average consistency algorithm,under the condition of Slater,we obtain a constant step method convergence boundary.Finally,the effectiveness of the method is proved by simulation examples.The specific details are as follows:1.When the communication cost between sensors in the network is fixed,we design a random gradient-free saddle point algorithm to solve the distributed network optimization problem.Considering that the cost function of the agent is usually a convex function,we design a Lagrangian function for the convex-concave function,and obtain the Lagrangian approximation saddle point.Then we consider that the saddle point algorithm based on the subgradient method is required for the function,and it is very difficult to adopt the subgradient method for some non-smooth functions.In this regard,we further improved the saddle point algorithm and designed a saddle point algorithm based on random gradient free.After several iterations,we analyzed the convergence of the results.2.Based on the above work,we analyze the situation of time-varying network connections.When the communication cost between agents is time-varying,we still use the random gradient-free saddle point algorithm to solve the distributed optimization problem.Finally,the convergence of the results is analyzed.3.In the digital communication environment,due to the limitation of the channel capacity of the communication channel,even if the state of each agent is a continuous value,only a limited number of bits of information can be transmitted between adjacent agents in each communication..That is to say,all the information received or transmitted between the agents is the quantized information.This means we need to quantify before we transfer the information.In order to enable accurate transmission of information,we analyze the quantization accuracy and quantize the objective function.It turns out that the result converges to the optimal value.