Risk-sensitive Semi-Markov Decision Problems with Discounted Cost and General Utilities

TL;DR

This paper develops a framework for risk-sensitive control of semi-Markov processes with general utilities, providing characterizations of value functions and optimal controls for both finite and infinite horizons.

Contribution

It introduces a novel approach using state augmentation to handle risk-sensitive criteria with general utility functions in semi-Markov decision processes.

Findings

Characterization of value functions for risk-sensitive semi-Markov control.

Derivation of optimal controls using state augmentation.

Applicability to both finite and infinite horizon problems.

Abstract

In this article we consider risk-sensitive control of semi-Markov processes with a discrete state space. We consider general utility functions and discounted cost in the optimization criteria. We consider random finite horizon and infinite horizon problems. Using a state augmentation technique we characterise the value functions and also prescribe optimal controls.