Second Order Optimality in Markov and Semi-Markov Decision Processes

0517875 - ÚTIA 2020 RIV CZ eng K - Conference Paper (Czech conference)
Sladký, Karel
Second Order Optimality in Markov and Semi-Markov Decision Processes.
Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019. České Budějovice: University of South Bohemia in České Budějovice, Faculty of Economics, 2019 - (Houda, M.; Remeš, R.), s. 338-343. ISBN 978-80-7394-760-6.
[MME 2019: International Conference on Mathematical Methods in Economics /37./. České Budějovice (CZ), 11.09.2019-13.09.2019]
R&D Projects: GA ČR GA18-02739S
Institutional support: RVO:67985556
Keywords : semi-Markov processes with rewards * discrete and continuous-time Markov reward chains * risk-sensitive optimality * average reward and variance over time
OECD category: Statistics and probability
http://library.utia.cas.cz/separaty/2019/E/sladky-0517875.pdf

Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per time may be quite insufficient to characterize the problem from the point of a decision maker. To this end it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean-variance selection rules, i.e. we optimize the weighted sum of average or total reward and its variance. Such approach has been already studied for very special classes of semi-Markov decision processes, in particular, for Markov decision processes in discrete - and continuous-time setting. In this note these approaches are summarized and possible extensions to the wider class of semi-Markov decision processes is discussed. Attention is mostly restricted to uncontrolled models in which the chain is aperiodic and contains a single class of recurrent states. Considering finite time horizons, explicit formulas for the first and second moments of total reward as well as for the corresponding variance are produced.
Permanent Link: http://hdl.handle.net/11104/0303159