论文标题
基于Lyapunov的人机相互作用的量子决策系统的随机稳定性
Lyapunov based Stochastic Stability of a Quantum Decision System for Human-Machine Interaction
论文作者
论文摘要
在数学心理学中，决策者是使用量子力学的Lindbladian方程来建模的，以捕获重要的以人为中心的特征，例如订单效应和违反确定的事物原则。我们考虑涉及量子决策者（人）和控制器（机器）的人机相互作用。考虑到一系列人类的决策，随着时间的推移，控制器如何动态提供输入消息以适应这些决策以融合特定的决策？我们通过新颖的随机Lyapunov论证表明，如何控制量子决策者的lindbladian动力学，以渐进地收敛到特定的决策。我们的方法为人类传感器决策提供了一个有用的数学框架。随机Lyapunov的结果也具有独立的兴趣，因为它们概括了文献中的最新结果。
In mathematical psychology, decision makers are modeled using the Lindbladian equations from quantum mechanics to capture important human-centric features such as order effects and violation of the sure thing principle. We consider human-machine interaction involving a quantum decision maker (human) and a controller (machine). Given a sequence of human decisions over time, how can the controller dynamically provide input messages to adapt these decisions so as to converge to a specific decision? We show via novel stochastic Lyapunov arguments how the Lindbladian dynamics of the quantum decision maker can be controlled to converge to a specific decision asymptotically. Our methodology yields a useful mathematical framework for human-sensor decision making. The stochastic Lyapunov results are also of independent interest as they generalize recent results in the literature.
