turkmath.org

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)