Rational Inattention, Stochastic Control and Rate-Distortion Theory

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Event Speaker: 

Maxim Raginsky (UIUC)

Event Location: 

32-155

Event Date/Time: 

Tuesday, April 9, 2013 - 4:00pm

Reception to follow.
 
Abstract:
The framework of rational inattention, proposed by the economist Christopher Sims, studies decision-making by agents who minimize expected cost given available information (hence “rational”), but are capable of handling only a limited amount of information (hence “inattention”). Quantitatively, this information-processing constraint is stated in terms of an upper bound on the Shannon mutual information between the state of the system and the observation available to the agent. However, most of existing work on rational inattention has been relying on heuristic arguments and various simplifying assumptions on the structure of observation channels.

In this talk, based on joint work with Ehsan Shafieepoorfard and Sean Meyn, I will present a general theory of dynamic decision-making subject to information constraints in the context of average-cost optimal control of Markov processes. The underlying optimization problem can be reduced to an infinite-dimensional convex program fundamentally related to rate-distortion theory. In particular, it will be shown that the optimal information-constrained controller is the solution of a certain Shannon rate-distortion problem where the distortion function is given by the Bellman error, a quantity that naturally arises in approximate dynamic programming. The usual solution of the average-cost control problem, given by the Average-Cost Optimality Equation, is recovered in the information-unconstrained limit. The general theory will be illustrated through the example of scalar linear-quadratic-Gaussian (LQG) control in the rational inattention regime.

Biography:
Maxim Raginsky received the B.S. and M.S. degrees in 2000 and the Ph.D. degree in 2002 from Northwestern University, Evanston, IL, all in electrical engineering. He has held research positions with Northwestern, the University of Illinois at Urbana-Champaign (where he was a Beckman Foundation Fellow from 2004 to 2007), and Duke University. In 2012, he has returned to UIUC, where he is currently an Assistant Professor with the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory. In 2013, Prof. Raginsky has received a Faculty Early Career Development (CAREER) Award from the National Science Foundation. His research interests lie at the intersection of information theory, machine learning, and control.