题目：Multivariate Rational Inattention
摘要：We study optimal control problems in the multivariate linear-quadratic-Gaussian framework under rational inattention and show that the multivariate attention allocation problem can be reduced to a dynamic tracking problem in information theory. We propose a general solution method to solve this problem by using rate distortion functions and semidefinite programming and derive the optimal form and dimension of signals without strong prior restrictions. We provide generalized reverse water-filling solutions for some special cases. Applying our method to solve three multivariate economic models, we obtain some results qualitatively different from the literature.