Online Parameter Identification of Cost Functions in Generalized Nash Games

• 成果类型: Article
• 署名作者: Chen, Jianguo; Lei, Jinlong; Hong, Yiguang; Qi, Hongsheng
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Tongji University; Tongji University; Tongji University; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3610251
• 发表日期: 2026
• 关键词: equilibrium

摘要

This work studies the online parameter identification of cost functions in a generalized Nash game, where each player's cost function is influenced by an observable signal and some unknown parameters. A learner can sequentially observe the equilibria reached by the game system as the observable signal changes, and its goal is to identify the unknown parameters in the cost functions. We recast this problem as an online optimization and introduce a novel online parameter identification algorithm. To be specific, we construct a regularized loss function that balances between conservativeness and correctiveness, where the conservativeness term ensures that the renewed estimates do not deviate significantly from the current estimates, while the correctiveness term is captured by the Karush-Kuhn-Tucker conditions of the generalized Nash equilibrium. For which, the balance is adjusted by a learning rate parameter. We then prove that when the players' cost functions are linear with respect to the unknown parameters and the learning rate satisfies mu(k )proportional to 1/root k, along with other assumptions, the regret bound of the proposed algorithm is O(root K) (k and K represent the current round of online algorithm and the total rounds of games played, respectively). Finally, we conduct numerical simulations on the parameter identification of a Nash-Cournot problem to demonstrate that the performance of our proposed online algorithm is comparable to that of the offline setting.