Bayesian Persuasion With State-Dependent Quadratic Cost Measures
Bayesian Persuasion With State-Dependent Quadratic Cost Measures
复制标题
贝叶斯说服与状态相关的二次成本测量
DOI：
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发表时间：
2019
影响因子：
6.8
通讯作者：
T. Başar
中科院分区：
文献类型：
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作者：
M. O. Sayin;T. Başar
在这篇文章中，我们解决贝叶斯说服发送者和接收者之间的状态依赖的二次成本措施的一般类分布。接收方试图根据发送方发送的信号对状态进行均方误差估计，而发送方则有策略地发送信号，以便以某种方式控制接收方的估计。这种方案可以模拟，例如，欺骗和隐私，多智能体系统中的问题。现有的解决方案的概念是不可行的，因为这里的接收器具有连续的动作空间。我们表明，对于有限的状态空间，最佳的信令策略可以通过一个等价的线性优化问题的锥上的完全正矩阵计算。然后，我们建立其强对偶的一个共正计划。为了验证这一等价结果的有效性，我们采用了完全正锥的序贯多面体逼近，并对其性能进行了数值分析。我们还量化了一个连续分布的量化版本的近似误差，并表明，一个半定的程序放松的等价问题可能是一个基准下限发送者的成本为大的状态空间。
In this article, we address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receiver’s estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multiagent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the sender’s cost for large state spaces.