Chapter

Whittle's Indexation Approach to and Applications of Bi-Objective Two-State Binary-Action Markov Decision Processes

December 2015

In book: Modern Trends in Controlled Stochastic Processes, Theory and Applications, Volume II (pp.140-151)
Publisher: Luniver Press
Editors: Alexey B. Piunovskiy

Authors:

Lancaster University

Vladimír Novák

National Bank of Slovakia

In this chapter we present how the Whittle's indexation approach, originally developed for the restless bandits problem, can be used to address multi-objective stochastic optimization problems. For clarity, we focus on Markov decision processes with two objectives, two states and two actions, and provide an optimal solution in terms of Whittle indices. We then broadly discuss the applications of our solution in optimal scheduling of queueing systems with abandonments and optimal choice of venture capitalists investments. We believe there is a need to develop the Whittle index theory further in order to tackle more general multi-objective problems.

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