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arXiv 2009.14730cs.GTcs.LG
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学习和强真实多任务同伴预测:变分方法

Learning and Strongly Truthful Multi-Task Peer Prediction: A Variational Approach

University of Michigan(密歇根大学);Harvard University(哈佛大学)

Grant Schoenebeck, Fang-Yi Yu

摘要:

同伴预测机制通过将代理的报告与他们的同伴的报告进行比较,激励代理即使在没有验证的情况下也如实地报告他们的信号。在无细节的多任务环境中,智能体对多个独立同分布的任务进行响应,并且该机制不知道智能体信号的先验分布。我们的目标是提供一个$ε$ -强真实的机制,诚实的奖励代理“严格”比任何其他策略配置文件(与$ε$添加剂错误),并这样做,而需要尽可能少的任务。我们设计了一个家庭的机制与评分功能,将一对报告的分数。如果评分函数是“先验理想”,则该机制是强真实的,并且只要评分函数足够接近理想的,则$ε$ -强真实。这将上述机制设计问题简化为学习问题--具体地说,学习理想的评分函数。我们利用这种减少来获得以下三个结果。1)我们将展示如何获得良好的界限所需的不同类型的先验任务的数量。我们的减少适用于无数的连续信号空间设置。这是第一个针对多任务设置设计的连续信号的对等预测机制。2)我们将展示如何将一个代理的信号(给定其他代理的信号)的软预测器转换为一种机制。这允许实际使用机器学习算法,即使在许多代理提供噪声信息时也能给出良好的结果。3)对于有限信号空间,我们得到了任意随机相关先验的$ε$ -强真实机制,它是最大可能先验。相比之下,先前的工作只实现了较弱的真实性概念(知情真实性)或需要对先前的假设更强。

英文摘要:

Peer prediction mechanisms incentivize agents to truthfully report their signals even in the absence of verification by comparing agents' reports with those of their peers. In the detail-free multi-task setting, agents respond to multiple independent and identically distributed tasks, and the mechanism does not know the prior distribution of agents' signals. The goal is to provide an $ε$-strongly truthful mechanism where truth-telling rewards agents "strictly" more than any other strategy profile (with $ε$ additive error), and to do so while requiring as few tasks as possible. We design a family of mechanisms with a scoring function that maps a pair of reports to a score. The mechanism is strongly truthful if the scoring function is "prior ideal," and $ε$-strongly truthful as long as the scoring function is sufficiently close to the ideal one. This reduces the above mechanism design problem to a learning problem -- specifically learning an ideal scoring function. We leverage this reduction to obtain the following three results. 1) We show how to derive good bounds on the number of tasks required for different types of priors. Our reduction applies to myriad continuous signal space settings. This is the first peer-prediction mechanism on continuous signals designed for the multi-task setting. 2) We show how to turn a soft-predictor of an agent's signals (given the other agents' signals) into a mechanism. This allows the practical use of machine learning algorithms that give good results even when many agents provide noisy information. 3) For finite signal spaces, we obtain $ε$-strongly truthful mechanisms on any stochastically relevant prior, which is the maximal possible prior. In contrast, prior work only achieves a weaker notion of truthfulness (informed truthfulness) or requires stronger assumptions on the prior.

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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