Approximation of target problems in Blackwell spaces

TL;DR

This paper develops a method to approximate target problems in weakly Blackwell spaces using Markov chains, demonstrating convergence to optimal solutions and illustrating the approach with a computational example.

Contribution

It introduces a new approximation technique for target problems in weakly Blackwell spaces and proves convergence under various pseudometrics.

Findings

Markov chain approximation converges to the optimal reduced problem

Method applies to problems involving information compression

Provides a computational example demonstrating practical application

Abstract

On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics. A computational example of compression of information is discussed.