Rational inattention in control of Markov chains

Markov Chain;Information Theory;Control;Limited capacity;Optimization

Shafieepoorfard, Ehsan ; Raginsky ; Maxim

关键词: Markov Chain;    Information Theory;    Control;    Limited capacity;    Optimization;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/72985/Ehsan_Shafieepoorfard.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis poses a general model for optimal control subject to informationconstraint, motivated in part by recent work on information-constraineddecision-making by economic agents.In the average-cost optimal control framework, the general model introducedin this paper reduces to a variant of the linear-programming representationof the average-cost optimal control problem, subject to an additionalmutual information constraint on the randomized stationary policy. The resultingin nite-dimensional convex program admits a decomposition basedon the Bellman error, which is the subject of study in approximate dynamicprogramming.Later, we apply the general theory to an information-constrained variantof the scalar Linear-Quadratic-Gaussian (LQG) control problem. We givean upper bound on the optimal steady-state value of the quadratic performanceobjective and present explicit constructions of controllers that achievethis bound. We show that the obvious certainty-equivalent control policy issuboptimal when the information constraints are very severe, and proposeanother policy that performs better in this low-information regime. In thetwo extreme cases of no information (open-loop) and perfect information,these two policies coincide with the optimum.