Distributed Stochastic Approximation Algorithms and Heavy-Tailed Age of Information

2026-09-23

AI Summary

研究在多智能体系统中，针对具有重尾特性的信息新鲜度（AoI）问题，分析了分布式随机逼近算法的稳定性和收敛性。

Abstract

Algorithms in multi-agent systems such as federated learning, mobile robotic swarming, and consensus control can be designed and analyzed as distributed stochastic approximation algorithms. Such algorithms involve information exchanges between agents for various computations. The freshness of the information can be quantified using the Age of Information (AoI) metric. Consider robotic teams operating in highly obstructed geographical settings, such as subterranean or dense urban environments. Because of spatial disconnections, AoI has empirically been observed to be heavy-tailed with unbounded moments. However, most analyses assume AoI with bounded moments, creating a gap between theory and practice. To the best of our knowledge, ours is the first analysis under general heavy-tailed AoI with potentially infinite mean. We study the stability (almost sure boundedness of the distributed iterates) and convergence of multi-agent systems that are strictly dissipative in the scaling limit (system at ``infinity''). Examples include most gradient-based and consensus algorithms under the Robbins-Monro step-size regime.

Problem

• Distributed Stochastic Approximation
• Heavy-Tailed Age of Information
• Multi-Agent Systems
• Information Freshness

Innovation

• Distributed Stochastic Approximation
• Heavy-Tailed Age of Information
• Multi-Agent Systems
• Stability and Convergence