Inverse Learning of Black-Box Aggregator for Robust Nash Equilibrium

• 成果类型: Article
• 署名作者: Chen, Guanpu; Xu, Gehui; He, Fengxiang; Tao, Dacheng; Parisini, Thomas; Johansson, Karl Henrik
• 署名单位: Royal Institute of Technology; Imperial College London; University of Edinburgh; Nanyang Technological University; Aalborg University; University of Trieste
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3634219
• 发表日期: 2026
• 关键词: randomized solutions; algorithms

摘要

In this article, we study the robustness of the Nash equilibrium (NE) in aggregative games with coupling constraints. When the constraint parameters are uncertain, the associated NE might be perturbed. It is essential to find a robust NE satisfying all possible constraints affected by the uncertain parameters. Although some methods have been developed for robust NE, these results rely on complete information about the game. We instead consider a scenario when only the uncertain parameters and associated perturbed NE are available, but the players' weights in the aggregator are unknown. With the uncertain parameters and perturbed NE constituting data, we propose data-based optimization to inversely learn players' weights in the black-box aggregator. We then use the learned weights in a transformed augmented problem without uncertainty and derive the first-order conditions for computing the robust NE. Furthermore, we characterize the generalization guarantee of the proposed learning approach in terms of violation probability.