Decentralized Concurrent Learning with Coordinated Momentum and Restart

TL;DR

This paper introduces a novel decentralized concurrent learning algorithm with coordinated momentum and restart, ensuring stability and improved transient performance in multi-agent systems with directed communication networks.

Contribution

It provides a theoretical framework for stable restart policies in decentralized learning with directed graphs, using graph theory and hybrid systems tools.

Findings

Achieves robust asymptotic stability under certain data richness conditions.

Demonstrates improved transient performance with coordinated periodic restart.

Validates theoretical results through three practical multi-agent applications.

Abstract

This paper studies the stability and convergence properties of a class of multi-agent concurrent learning (CL) algorithms with momentum and restart. Such algorithms can be integrated as part of the estimation pipelines of data-enabled multi-agent control systems to enhance transient performance while maintaining stability guarantees. However, characterizing restarting policies that yield stable behaviors in decentralized CL systems, especially when the network topology of the communication graph is directed, has remained an open problem. In this paper, we provide an answer to this problem by synergistically leveraging tools from graph theory and hybrid dynamical systems theory. Specifically, we show that under a cooperative richness condition on the overall multi-agent system's data, and by employing coordinated periodic restart with a frequency that is tempered by the level of asymmetry of the communication graph, the resulting decentralized dynamics exhibit robust asymptotic stability properties, characterized in terms of input-to-state stability bounds, and also achieve a desirable transient performance. To demonstrate the practical implications of the theoretical findings, three applications are also presented: cooperative parameter estimation over networks with private data sets, cooperative model-reference adaptive control, and cooperative data-enabled feedback optimization of nonlinear plants.