Distributed GNEP Algorithms without Multiplier Sharing and Applications to Multi-Robot Coordination and Contextual Bandit-Based Active Learning
For multi-agent systems with shared constraints, this work reduces communication overhead and enhances privacy in distributed GNEP solving, while the active learning part addresses the practical challenge of reducing labeling costs by adaptively selecting strategies.
This work introduces fully distributed continuous-time algorithms for Generalized Nash Equilibrium Problems (GNEPs) that converge without requiring multiplier exchange, reducing information exchange and improving privacy. The method converges to general GNEs and is demonstrated on multi-robot coordination. Additionally, a contextual bandit-based approach for adaptive active learning strategy selection is proposed and validated on public datasets.
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.