Distributed Heterogeneous Multi-Agent Optimization with Stochastic Sub-Gradient

• Published in: Journal of systems science and complexity Vol. 37; no. 4; pp. 1470 - 1487
• Main Authors: Hu, Haokun, Mo, Lipo, Cao, Xianbing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Algorithms; Complex Systems; Control; Graph theory; Martingales; Mathematics; Mathematics and Statistics; Mathematics of Computing; Multiagent systems; Operations Research/Decision Theory; Optimization; Reagents; Statistics; Systems Theory; Topology; distributed stochastic optimization; heterogeneous networks; Communication noises; sub-gradient measurement noises
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-024-2149-9

This paper studies the optimization problem of heterogeneous networks under a time-varying 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.