We study preference learning through recommendations in multi-agent game settings, where a moderator repeatedly interacts with agents whose utility functions are unknown. In each round, the moderator issues action recommendations and observes whether agents follow or deviate from them. We consider two canonical behavioral feedback models-best response and quantal response-and study how the information revealed by each model affects the learnability of agents' utilities. We show that under quantal-response feedback the game is learnable, up to a positive affine equivalence class, with logarithmic sample complexity in the desired precision, whereas best-response feedback can only identify a larger set of agents' utilities. We give a complete geometric characterization of this set. Moreover, we introduce a regret notion based on agents' incentives to deviate from recommendations and design an online algorithm with low regret under both feedback models, with bounds scaling linearly in the game dimension and logarithmically in time. Our results lay a theoretical foundation for AI recommendation systems in strategic multi-agent environments, where recommendation compliances are shaped by strategic interaction.

翻译：我们研究多智能体博弈环境下的偏好学习问题，其中协调者需与效用函数未知的智能体进行重复交互。在每一轮中，协调者发布行动建议，并观察智能体选择遵循还是偏离该建议。我们考虑两种经典行为反馈模型——最优响应与量化响应，并探究每种模型所揭示的信息如何影响智能体效用函数的可学习性。研究表明，在量化响应反馈下，博弈可在期望精度内以对数级样本复杂度学习到正仿射等价类；而最优响应反馈仅能识别更大范围的智能体效用函数集合。我们对该集合给出了完整的几何特征描述。此外，我们基于智能体偏离建议的动机提出新的遗憾定义，并设计出适用于两种反馈模型的在线算法，其遗憾界随博弈维度呈线性增长、随时间呈对数增长。本研究成果为战略多智能体环境中的AI推荐系统奠定了理论基础，其中推荐依从性由战略交互行为所塑造。