The classical textbook treatment of optimal stochastic control relies on the "classical" information structure, wherein the controllers are co-located and have the same information about the state. For linear systems with quadratic cost and Gaussian noise, this leads to a very clean result—an optimal controller that is linear in state. This might raise the hopes that such results can be pushed a little further, but these hopes were dashed by a famous counterexample by Witsenhausen, a scientist in Bell Labs, who showed that a simple two stage problem with non-classical information structure fails to have a linear optimal controller. This still left open the issue of what the optimal controller is for this problem. Bansal and Basar considered a more tractable variant using the data processing inequality (DPI) from information theory. This talk will argue that this is a special case of a more general paradigm and the role of DPI is precisely that of "convexifying" a non-convex optimization problem. Thus we have a _menage a trois_ of stochastic control, information theory and convex optimization.
Ankur is an Assistant Professor with the Systems and Control Engineering group at IIT Bombay and a recipient of the INSPIRE Faculty Award of the Department of Science and Technology, Government of India, 2013. He received his B.Tech. in Aerospace Engineering from IIT Bombay in 2006, M.S. in General Engineering in 2008 and Ph.D. in Industrial Engineering in 2010, both from the University of Illinois at Urbana-Champaign (UIUC). From 2010-2012 he was a post-doctoral researcher at the Coordinated Science Laboratory at UIUC. His research interests include game theory and economics, optimization and variational inequalities, combinatorial coding theory problems, the role of information in stochastic control, and operations research.