arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.02873cs.GT
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面向信息获取的在线机制设计

Online Mechanism Design for Information Acquisition

Federico Cacciamani, Matteo Castiglioni, Nicola Gatti

AI总结:

该研究针对信息获取场景的机制设计问题,提出了最优激励相容机制的高效计算方法,并针对全反馈与老虎机反馈两种在线场景给出带 regret 与约束违反量保证的算法及紧下界。

摘要:

我们研究信息获取场景下的机制设计问题。该场景刻画了不知情的接收者与一组知情的发送者之间的策略互动。在我们的模型中,发送者获取关于自然潜在状态的信息,并将其观测结果(如实或不实)传达给接收者,接收者基于这些信息选择行动。我们的目标是设计既能最大化接收者效用,又能激励发送者如实报告信息的机制。首先,我们提出一种算法,可高效计算最优的激励相容(IC)机制。随后,我们聚焦于在线问题:接收者在未知博弈中进行序贯互动,目标是最小化相对于最优IC机制的累积遗憾,以及激励相容约束的累积违反量。我们研究了两种不同的在线场景,即全反馈和老虎机反馈(bandit feedback)设置。对于全反馈问题,我们提出的算法可保证$\tilde{\boldsymbol{\textit{O}}}(\boldsymbol{\textit{√}}\boldsymbol{\textit{T}})$的遗憾与违反量;对于老虎机反馈设置,我们提出的算法对任意$\boldsymbol{\textit{α}}\boldsymbol{\textit{∈}}[1/2, 1]$,可达到$\tilde{\boldsymbol{\textit{O}}}(\boldsymbol{\textit{T}}^\boldsymbol{\textit{α}})$的遗憾与$\tilde{\boldsymbol{\textit{O}}}(\boldsymbol{\textit{T}}^{1-\boldsymbol{\textit{α}}/2})$的违反量。最后,我们给出了紧的下界,对研究结果进行了补充。

英文摘要:

We study the problem of designing mechanisms for \emph{information acquisition} scenarios. This setting models strategic interactions between an uniformed \emph{receiver} and a set of informed \emph{senders}. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal \emph{incentive compatible} (IC) mechanism. Then, we focus on the \emph{online} problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the \emph{cumulative regret} w.r.t. the optimal IC mechanism, and the \emph{cumulative violation} of the incentive compatibility constraints. We investigate two different online scenarios, \emph{i.e.,} the \emph{full} and \emph{bandit feedback} settings. For the full feedback problem, we propose an algorithm that guarantees $\tilde{\mathcal O}(\sqrt T)$ regret and violation, while for the bandit feedback setting we present an algorithm that attains $\tilde{\mathcal O}(T^α)$ regret and $\tilde{\mathcal O}(T^{1-α/2})$ violation for any $α\in[1/2, 1]$. Finally, we complement our results providing a tight lower bound.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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