We study a sequential mechanism design problem in which a principal seeks to elicit truthful reports from multiple rational agents while starting with no prior knowledge of agents' beliefs. We introduce Distributionally Robust Adaptive Mechanism (DRAM), a general framework combining insights from both mechanism design and online learning to jointly address truthfulness and cost-optimality. Throughout the sequential game, the mechanism estimates agents' beliefs and iteratively updates a distributionally robust linear program with shrinking ambiguity sets to reduce payments while preserving truthfulness. Our mechanism guarantees truthful reporting with high probability while achieving $\tilde{O}(\sqrt{T})$ cumulative regret, and we establish a matching lower bound showing that no truthful adaptive mechanism can asymptotically do better. The framework generalizes to plug-in estimators, supporting structured priors and delayed feedback. To our knowledge, this is the first adaptive mechanism under general settings that maintains truthfulness and achieves optimal regret when incentive constraints are unknown and must be learned.

翻译：本文研究一个序贯机制设计问题，其中委托方试图从多个理性智能体处获取真实报告，且初始时对智能体的信念一无所知。我们提出了分布鲁棒自适应机制（DRAM），这是一个结合机制设计与在线学习思想的通用框架，旨在同时解决真实性与成本最优性问题。在整个序贯博弈过程中，该机制通过估计智能体的信念，并迭代更新一个具有收缩模糊集的分布鲁棒线性规划，以在保持真实性的同时减少支付。我们的机制以高概率保证真实报告，同时实现$\tilde{O}(\sqrt{T})$的累积遗憾，并且我们建立了一个匹配的下界，表明任何真实的自适应机制在渐近意义上无法做得更好。该框架可推广至插件估计器，支持结构化先验和延迟反馈。据我们所知，这是在激励约束未知且必须学习的通用设置下，首个能保持真实性并达到最优遗憾的自适应机制。