带事件触发机制的分布式量化随机无梯度投影算法

Distributed quantized random gradient-free algorithm with event triggered communication

本文研究多智能体系统的分布式约束优化问题,系统中的每个智能体仅知道自身的局部目标函数和全局非空约束集,通过与邻居节点进行信息交互,最终协同求出优化问题的最优解.本文所提出的算法针对通信网络为时变不平衡有向图,且每个智能体不知道它的出度的情况.同时考虑到现实中通信带宽有限和通讯成本的限制,应用基于编译码方案的量化技术对节点之间的通讯信息进行预处理,再利用事件触发广播技术降低网络的通信次数.同时引入高斯光滑函数和随机无梯度方法替代传统的次梯度方法.本文提出了基于事件触发的分布式量化随机无梯度算法,在目标函数为凸且Lipschitz连续的条件下,证明了所提算法能收敛到最优值的邻域,同时给出了使量化器不饱和量化水平更新规则.最后通过数值仿真验证了算法的有效性和可行性.

We study the distributed constraint optimization problem of multi-agent systems,where each agent only knows its own local objective function and a global non-empty constraint set and the optimal solution of the optimization problem is finally obtained by communicating with neighbor nodes.The proposed algorithm is for the case that the communication network is time-varying unbalanced digraphs and each agent does not know its out-degree.Considering the limited bandwidth and communication cost in reality,the quantization technology based on coding and decoding scheme is used to preprocess the communication information between nodes and the event triggered broadcasting technology is also used to reduce the communication times of the networks.Gaussian smooth function and gradient-free oracle are introduced to replace the traditional subgradient method in this paper.We propose a distributed quantized random gradient-free algorithm based on event triggering communication,and under the condition that the objective function is convex and Lipschitz continuous,it is proved that the proposed algorithm can converge to the neighborhood of the optimal value.Furthermore,the update rule of quantization level that makes the quantizer unsaturated is given.Finally,numerical simulations are provided to illustrate the validity and feasibility of the algorithm.