**Department of Mathematics**

**"****Approximate Optimality of Finite Models in Stochastic
and Decentralized Control****"**

**NACİ SALDİ**

**(University of Illinois at
Urbana-Champaign)**

**Abstract: **For
stochastic control problems with uncountable state and action spaces, the
computation of optimal policies is known to be prohibitively hard. In this
talk, we will present conditions under which finite models obtained through
quantization of the state and action sets can be used to construct
approximately optimal policies. Under further conditions, we obtain explicit
rates of convergence to the optimal cost of the original problem as the
quantization rate increases. We then extend our analysis to decentralized
stochastic control problems, also known as team problems, which are
increasingly important in the context of networked control systems. We show
that for a large class of sequential team problems one can construct a sequence
of finite models obtained through the quantization of measurement and action spaces
whose solutions constructively converge to the optimal cost. The celebrated
counterexample of Witsenhausen is an important
special case that will be discussed in detail. (Joint work with Serdar Yuksel and Tamas Linder).

**Date: ****Wednesday, October 12, 2016**

**Time: ****11.40**

**Place: ****Mathematics Seminar Room,
SA-141**