设计了一种能自适应学习并保持诚实上报的多智能体激励机制。
Multi-agent Adaptive Mechanism Design
- 结合机制设计与在线学习，动态更新不确定集以减少支付
- 在未知激励约束下实现近似最优的累计后悔（˜O(√T)）
- 适用于结构化先验和延迟反馈，适合需长期博弈的系统
我们研究了一个序贯机制设计问题，其中主事者需从多个理性代理中获取真实报告，且初始时对代理信念一无所知。本文提出分布鲁棒自适应机制（DRAM），融合机制设计与在线学习思想，同时保障诚实性与成本最优。在序贯博弈过程中，机制估计代理信念，并通过不断缩小不确定性集来迭代优化分布鲁棒线性规划，从而降低支付并维持诚实性。该机制以高概率保证诚实上报，实现˜O(√T)的累计后悔，且我们建立了匹配的下界，表明任何可行的自适应机制均无法在渐近意义下表现更优。该框架可适配插值估计器，支持结构化先验与延迟反馈。据我们所知，这是首个在激励约束未知且需学习的通用设定下，既保持诚实性又达到最优后悔率的自适应机制。
原文摘要 · Abstract (English)
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 feasible 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.
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