Optimization and convergence of observation channels in stochastic control

This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence, continuity, and convexity properties are investigated. Continuity properties of the optimal cost in channels are explored under total variation, setwise convergence and weak convergence. Sufficient conditions for sequential compactness under total variation and setwise convergence are presented. It is shown that the optimization is concave in observation channels. This implies that the optimization problem is non-convex in quantization/coding policies for a class of networked control problems. Furthermore, the paper explains why a class of decentralized control problems, under the non-classical information structure, is non-convex when signaling is present.