Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters

TL;DR

This paper explores multi-objective optimization for Markov decision processes with uncertain parameters, aiming to find policies that perform well across various scenarios rather than optimizing for worst-case or average-case alone.

Contribution

It introduces methods for computing Pareto optimal policies in bounded-parameter MDPs considering multiple performance scenarios simultaneously.

Findings

Developed algorithms for Pareto optimal policy computation.

Analyzed worst, best, and average case performances together.

Demonstrated effectiveness on bounded-parameter MDPs.

Abstract

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, the lowest upper bound on costs). However, hedging against an unlikely worst case may lead to losses in other situations. In general, one is interested in policies that behave well in all situations which results in a multi-objective view on decision making. In this paper, we consider policies for the expected discounted reward measure of MDPs with uncertain parameters. In particular, the approach is defined for bounded-parameter MDPs (BMDPs) [8]. In this setting the worst, best and average case performances of a policy are analyzed simultaneously, which yields a multi-scenario multi-objective optimization problem. The paper presents and evaluates approaches to compute the pure Pareto optimal policies in the value vector space.