Blackwell optimality and policy stability for long-run risk sensitive stochastic control

TL;DR

This paper investigates the stability and robustness of optimal policies in long-run risk-sensitive stochastic control for finite MDPs, focusing on Blackwell optimality and the effects of perturbations to risk aversion.

Contribution

It establishes the connection between Blackwell optimality and risk-sensitive vanishing discount approximation, analyzing policy stability under parameter perturbations.

Findings

Optimal policies exhibit stability under small perturbations.

Blackwell optimality is linked to the vanishing discount framework.

Examples illustrate the complexities of risk-sensitive control.

Abstract

This paper analyzes the stability of optimal policies in the long-run stochastic control framework with an averaged risk-sensitive criterion for discrete-time MDPs on finite state-action space. In particular, we study the robustness of optimal controls when perturbations to the risk-aversion parameter are applied, and investigate the Blackwell property, together with its link to the risk-sensitive vanishing discount approximation framework. Finally, we present examples that help to better understand the intricacies of the risk-sensitive control framework.