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This research advances distributed optimization for multi-agent systems by introducing an input-to-state stability framework that eliminates the need for multiplier consensus, thereby enhancing privacy and reducing communication overhead. While rooted in control theory and game theory, the work directly impacts AI applications involving decentralized decision-making where traditional convergence guarantees often fail without shared Lagrange multipliers. The approach allows different initializations to converge to valid generalized Nash equilibria, offering a robust solution for complex engineering problems requiring distributed algorithms.
Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus
arXiv:2609.06983v1 Announce Type: cross Abstract: Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.
Abstract:Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.
6 pages, 1 figure. Accepted to CDC 2026
Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Multiagent Systems (cs.MA)
arXiv:2609.06983 [math.OC]
(or arXiv:2609.06983v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2609.06983 arXiv-issued DOI via DataCite (pending registration)
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