Rational inattention in control of Markov chains

This thesis poses a general model for optimal control subject to information constraint, motivated in part by recent work on information-constrained decision-making by economic agents. In the average-cost optimal control framework, the general model introduced in this paper reduces to a variant of the linear-programming representation of the average-cost optimal control problem, subject to an additional mutual information constraint on the randomized stationary policy. The resulting in nite-dimensional convex program admits a decomposition based on the Bellman error, which is the subject of study in approximate dynamic programming. Later, we apply the general theory to an information-constrained variant of the scalar Linear-Quadratic-Gaussian (LQG) control problem. We give an upper bound on the optimal steady-state value of the quadratic performance objective and present explicit constructions of controllers that achieve this bound. We show that the obvious certainty-equivalent control policy is suboptimal when the information constraints are very severe, and propose another policy that performs better in this low-information regime. In the two extreme cases of no information (open-loop) and perfect information, these two policies coincide with the optimum.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Shafieepoorfard, Ehsan

Contributors dc:contributor

• Raginsky, Maxim

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

Statement dc:rights

• Copyright 2014 Ehsan Shafieepoorfard

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72985

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72985