Generalized Nash Equilibrium Problems (GNEPs) arise in many applications, including non-cooperative multi-agent control problems. Although many methods exist for finding generalized Nash equilibria, most of them rely on assuming knowledge of the objective functions or being able to query the best responses of the agents. We present a method for learning solutions of GNEPs only based on querying agents for their preference between two alternative decisions. We use the collected preference data to learn a GNEP whose equilibrium approximates a GNE of the underlying (unknown) problem. Preference queries are selected using an active-learning strategy that balances exploration of the decision space and exploitation of the learned GNEP. We present numerical results on game-theoretic linear quadratic regulation problems, as well as on other literature GNEP examples, showing the effectiveness of the proposed method.

翻译：广义纳什均衡问题（GNEPs）广泛存在于诸多应用领域，包括非合作多智能体控制问题。尽管存在许多寻找广义纳什均衡的方法，但大多数都依赖于假设已知目标函数或能够查询智能体的最优响应。本文提出一种仅通过查询智能体对两个备选决策的偏好来学习GNEP解的方法。我们利用收集到的偏好数据学习一个GNEP，其均衡近似于底层（未知）问题的一个广义纳什均衡。偏好查询的选择采用一种主动学习策略，该策略平衡了对决策空间的探索与对已学习GNEP的利用。我们在博弈论线性二次调节问题以及其他文献中的GNEP示例上给出了数值结果，证明了所提方法的有效性。