Title: Multiplier-Free Distributed GNEP Algorithms: Applications in Multi-Robot Systems and Contextual Bandit Active Learning

Abstract

The evolution of artificial intelligence has broadened its scope beyond traditional optimization, increasingly incorporating equilibrium analysis within noncooperative games. A significant subset of these games is characterized by shared constraints, giving rise to Generalized Nash Equilibrium Problems (GNEPs). Traditional distributed solutions for these problems often rely on agents exchanging Lagrange multipliers to maintain consensus and calculate variational-GNEs (v-GNEs). This study presents fully distributed continuous-time algorithms that achieve convergence without the need for such multiplier exchange. By eliminating this requirement, the proposed method reduces the volume of information transmitted per iteration and enhances privacy. The theoretical analysis is centered on strongly monotone games featuring convex individual constraints alongside linear shared constraints. Furthermore, the paper details several discretization schemes derived from the continuous-time framework. Notably, the proposed approach converges to general GNEs rather than being limited to v-GNEs, with the specific equilibrium reached contingent upon the initial conditions. The practical utility of this method is illustrated through case studies in multi-robot coordination and placement.

In the second segment of this work, which is a collaboration with researchers from Amazon, the focus shifts to a critical challenge in real-world machine learning: the high cost and labor intensity of collecting labeled data. Active learning seeks to mitigate this burden by minimizing the need for manual labeling. However, conventional, handcrafted active learning strategies tend to excel only on specific dataset types, which are typically unknown beforehand. To address this limitation, the authors propose a framework that utilizes contextual bandits to dynamically select the most appropriate active learning strategy. The viability of this adaptive approach is validated using publicly available external datasets.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC