Optimization and Convergence of Observation Channels in Stochastic Control

TL;DR

This paper investigates how to optimize observation channels in stochastic control, focusing on existence, continuity, and compactness properties, with applications to quantization.

Contribution

It provides new results on the existence, continuity, and compactness of optimal observation channels in stochastic control problems.

Findings

Continuity of optimal cost under various convergence modes.

Sufficient conditions for compactness of channel classes.

Applications to quantization problems.

Abstract

This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence and continuity properties are investigated mostly (but not exclusively) concentrating on the single-stage case. Continuity properties of the optimal cost in channels are explored under total variation, setwise convergence, and weak convergence. Sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored.