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Title:Rational inattention in control of Markov chains
Author(s):Shafieepoorfard, Ehsan
Advisor(s):Raginsky, Maxim
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Markov Chain
Information Theory
Limited capacity
Abstract: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.
Issue Date:2015-01-21
Rights Information:Copyright 2014 Ehsan Shafieepoorfard
Date Available in IDEALS:2015-01-21
Date Deposited:2014-12

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