Department of Mathematics and Statistics
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).