Distributed Heterogeneous Multi-Agent Optimization with Stochastic Sub-Gradient  

作　　者：HU Haokun MO Lipo CAO Xianbing 

机构地区：[1]School of Mathematics and Statistics,Central South University,Changsha 410083,China [2]School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China [3]Research Centre for Agri-Product Quality Traceability,Beijing Technology and Business University,Beijing 100048,China [4]School of Computer and Artificial Intelligence,Beijing Technology and Business University,Beijing 100048,China [5]China Food Flavor and Nutrition Health Innovation Center,Beijing Technology and Business University,Beijing 100048,China

出　　处：《Journal of Systems Science & Complexity》2024年第4期1470-1487,共18页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.61973329;National Key Technology R&D Program of China under Grant No.2021YFD2100605;Project of Beijing Municipal University Teacher Team Construction Support Plan under Grant No.BPHR20220104。

摘　　要：This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents.To weaken the effect of these noises,two step sizes are introduced in the control protocol.By graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost surely.At last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.

关 键 词：Communication noises distributed stochastic optimization heterogeneous networks subgradient measurement noises 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]