Rational inattention in scalar LQG control

Abstract

Rational Inattention in Scalar LQG Control Ehsan Shafieepoorfard and Maxim RaginskyAhstract-Motivated in part by the "rational inattention" framework of information-constrained decision-making by eco nomic agents, we have recently introduced a general model for average-cost optimal control of Markov processes subject to mutual information constraints [1]. The optimal information constrained control problem reduces to an infinite-dimensional convex program and admits a decomposition based on the Bellman error, which is the object of study in approximate dynamic programming.In this paper, we apply our 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 exhibit 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.E. Shafieepoorfard and M. Raginsky are with the Department of Electri cal and Computer Engineering and the Coordinated Science Laboratory,

Sensing-Constrained LQG Control

“…Related literature includes approaches based on randomized sensor selection [9], dual volume sampling [10], [11], convex relaxations [12], [13], and submodularity [14]- [16]. The third set of related works is information-constrained (or informationregularized) LQG control [17], [18]. Shafieepoorfard and Raginsky [17] study rationally inattentive control laws for LQG control and discuss their effectiveness in stabilizing the system.…”

“…The third set of related works is information-constrained (or informationregularized) LQG control [17], [18]. Shafieepoorfard and Raginsky [17] study rationally inattentive control laws for LQG control and discuss their effectiveness in stabilizing the system. Tanaka and Mitter [18] consider the co-design of sensing, control, and estimation, propose to augment the standard LQG cost with an information-theoretic regularizer, and derive an elegant solution based on semidefinite programming.…”

Induced uncertainty, market price of risk, and the dynamics of consumption and wealth

“…30 The following proposition provides the expression of this relative volatility. 29 Estimating the process (45) on quarterly real nondurable and service consumption, logged and linearly detrended with R = 1.01, produces a nonstationary process (the autoregressive roots are 1.3038 and −0.3027), so we do not pursue this direction further. We note in passing that the estimate for θ is close to 0 and the estimate for Π is close to 1.…”

Minimum-information LQG control part I: Memoryless controllers

“…A special case of our current work was studied in [34]. Their setting is fully observable and scalar, whereas we treat the much more general setting of partially observable vector spaces.…”