Risk-sensitive Average Optimality in Markov Decision Processes

0502902 - ÚTIA 2019 RIV CS1 eng J - Článek v odborném periodiku
Sladký, Karel
Risk-sensitive Average Optimality in Markov Decision Processes.
Kybernetika. Roč. 54, č. 6 (2018), s. 1218-1230. ISSN 0023-5954.
[Mathematical Methods in Economy and Industry 2017. Jindřichův Hradec, 04.09.2017-06.09.2017]
Grant CEP: GA ČR GA18-02739S
Institucionální podpora: RVO:67985556
Klíčová slova: controlled Markov processes * risk-sensitive average optimality * asymptotic behavior
Obor OECD: Statistics and probability
Impakt faktor: 0.560, rok: 2018
http://library.utia.cas.cz/separaty/2019/E/sladky-0502902.pdf

In this note attention is focused on finding policies optimizing risk-sensitive optimality criteria in Markov decision chains. To this end we assume that the total reward generated by the Markov process is evaluated by an exponential utility function with a given risk-sensitive coefficient. The ratio of the first two moments depends on the value of the risk-sensitive coefficient, if the risk-sensitive coefficient is equal to zero we speak on risk-neutral models. Observe that the first moment of the generated reward corresponds to the expectation of the total reward and the second central moment of the reward variance. For communicating Markov processes and for some specific classes of unichain processes long run risk-sensitive average reward is independent of the starting state. In this note we present necessary and sufficient condition for existence of optimal policies independent of the starting state in unichain models and characterize the class of average risk-sensitive optimal policies.
Trvalý link: http://hdl.handle.net/11104/0295273