UTRC CDS Lecture: Serdar Yuksel, "Optimal quantization and quantized approximations"
Friday, April 10, 2015
1146 A V Williams
301 405 6576
United Technologies Research Center
Invited Lectures on Control and Dynamical Systems
Optimal Quantization and Quantized Approximations in Stochastic Control
Department of Mathematics and Statistics
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Quantization arises in networked control and stochastic control in the contexts of informational and computational constraints. In networked control, the goal is to characterize optimal quantization, coding and control policies under various performance criteria, such as some expected cost minimization or some stability criterion. In stochastic control, quantization also arises in developing approximate representations of Borel state/action space models with finite models, for discounted or average cost problems. Since for Markov Decision Processes with uncountable spaces the computation of optimal policies is known to be prohibitively hard, quantized models allow for tractable learning and computational algorithms. We will present general conditions under which finite models can be used to efficiently compute approximately optimal policies and obtain explicit and tight rates of convergence as the quantization rate increases. We will exhibit the information and probability theoretic connections between these two closely related problems, and design quantization algorithms that are optimal for the networked setup and order-optimal for the approximation setup. Some examples and future directions will be discussed. (Part of this work is joint with Naci Saldi and Tamas Linder).
Serdar Yuksel received his B.Sc. degree in Electrical and Electronics Engineering from Bilkent University in 2001; M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign in 2003 and 2006, respectively. He was a post-doctoral researcher at Yale University for a year before joining Queen's University as an Assistant Professor of Mathematics and Engineering in the Department of Mathematics and Statistics, where he is now an Associate Professor. He is the recipient of the 2013 CAIMS/PIMS Early Career Award in Applied Mathematics and an associate editor for the IEEE Transactions on Automatic Control.