A Linear-Quadratic Gaussian Approach to Dynamic Information Acquisition

European Journal of Operational Research, Vol. 270, No. 1, pp. 260--281, 2018

22 Pages Posted: 12 Oct 2015 Last revised: 1 Jun 2018

Thomas A. Weber

Ecole Polytechnique Federale de Lausanne - MTEI

Viet-Anh Nguyen

Ecole Polytechnique Federale de Lausanne - MTEI

Date Written: March 1, 2018

Abstract

We consider optimal information acquisition for the control of linear discrete-time random systems with noisy observations and apply the findings to the problem of dynamically implementing emissions-reduction targets. The optimal policy, which is provided in closed form, depends on a single composite parameter which determines the criticality of the system. For subcritical systems, it is optimal to perform “noise leveling,” that is, to reduce the variance of the state uncertainty to an optimal level and keep it constant by a steady feed of information updates. For critical systems, the optimal policy is “noise attenuation,” that is, to substantially decrease the variance once and never acquire information thereafter. Finally for supercritical systems, information acquisition is never in the best interest of the decision maker. In each case, an explicit expression of the value function is obtained. The criticality of the system, and therefore the tradeoff between spending resources on the control or on information to improve the control, is influenced by a “policy parameter” which determines the importance a decision maker places on uncertainty reduction. The dependence of the system performance on the policy parameter is illustrated using a practical climate-control problem where a regulator imposes state-contingent taxes to probabilistically attain emissions targets.

Keywords: Bayesian updating, Bellman equation, dynamic programming, emissions control, information acquisition, infinite-horizon optimal control, linear-quadratic systems, Markov decision problems, optimal filtering

JEL Classification: C11, C22, C54, C61, D81, D90, Q54, Q58

Suggested Citation

Weber, Thomas A. and Nguyen, Viet-Anh, A Linear-Quadratic Gaussian Approach to Dynamic Information Acquisition (March 1, 2018). European Journal of Operational Research, Vol. 270, No. 1, pp. 260--281, 2018. Available at SSRN: https://ssrn.com/abstract=2672271

Thomas A. Weber (Contact Author)

Ecole Polytechnique Federale de Lausanne - MTEI ( email )

Odyssea
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Lausanne, 1015
Switzerland
+41 (0)21 693 01 41 (Phone)
+41 (0)21 693 00 20 (Fax)

HOME PAGE: http://oes.epfl.ch

Viet-Anh Nguyen

Ecole Polytechnique Federale de Lausanne - MTEI ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

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