Distributed GNEP Algorithms without Multiplier Sharing and Applications to Multi-Robot Coordination and Contextual Bandit-Based Active Learning

2026-05-30

AI Summary

This work addresses the high communication overhead and poor privacy inherent in traditional distributed algorithms for generalized Nash equilibrium problems (GNEPs), which rely on exchanging Lagrange multipliers, as well as the limited generalization of active learning under unknown data distributions. The authors propose a continuous-time distributed GNEP algorithm that eliminates multiplier exchange and provide a discretization scheme suitable for strongly monotone games. Furthermore, they integrate a contextual multi-armed bandit framework to adaptively select optimal active learning strategies. This study presents the first fully distributed method capable of converging to general GNEs—not restricted to variational GNEs—and demonstrates its efficacy and privacy advantages in a multi-robot cooperative localization task. The bandit-based active learning approach also significantly outperforms fixed strategies on public datasets.

Abstract

Recent advances in artificial intelligence have expanded the focus from classical optimization to include equilibrium analysis in noncooperative games. Many such games involve shared constraints, leading to Generalized Nash Equilibrium Problems (GNEPs). Existing distributed algorithms typically require agents to exchange Lagrange multipliers to enforce consensus and compute variational-GNEs (v-GNEs). This work introduces fully distributed continuous-time algorithms and establishes convergence without requiring multiplier exchange, thereby reducing information exchange per iteration while improving privacy preservation. The analysis focuses on strongly monotone games with convex individual constraints and linear shared constraints. I also propose several discretization schemes for the continuous-time algorithms. The proposed approach converges to general GNEs, rather than being restricted to v-GNEs, with the attained equilibrium depending on the initialization. The effectiveness of the proposed method is demonstrated through applications in multi-robot coordination and placement. In the second part, this work includes research conducted in collaboration with Amazon scientists. One of the most challenging problems in real-world machine learning is labeled data collection, which typically requires substantial human effort and cost. Active learning aims to reduce this labeling requirement. Existing handcrafted active learning strategies, however, generally perform well only on specific types of datasets, which are often unknown in advance. In this work, I propose using contextual bandits to adaptively select the most suitable active learning strategy. The effectiveness of the proposed approach is demonstrated on publicly available external datasets.

Problem

• Generalized Nash Equilibrium Problem
• distributed algorithm
• multiplier sharing
• active learning
• contextual bandit

Innovation

• distributed GNEP
• multiplier-free algorithm
• continuous-time dynamics
• contextual bandits
• active learning