Risk-sensitive average optimality in Markov decision processes

Karel Sladký

Kybernetika (2018)

  • Volume: 54, Issue: 6, page 1218-1230
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Sladký, Karel. "Risk-sensitive average optimality in Markov decision processes." Kybernetika 54.6 (2018): 1218-1230. <http://eudml.org/doc/294578>.

@article{Sladký2018,
abstract = {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.},
author = {Sladký, Karel},
journal = {Kybernetika},
keywords = {controlled Markov processes; finite state space; asymptotic behavior; risk-sensitive average optimality},
language = {eng},
number = {6},
pages = {1218-1230},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Risk-sensitive average optimality in Markov decision processes},
url = {http://eudml.org/doc/294578},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Sladký, Karel
TI - Risk-sensitive average optimality in Markov decision processes
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 6
SP - 1218
EP - 1230
AB - 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.
LA - eng
KW - controlled Markov processes; finite state space; asymptotic behavior; risk-sensitive average optimality
UR - http://eudml.org/doc/294578
ER -

References

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Citations in EuDML Documents

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  1. Rubén Becerril-Borja, Raúl Montes-de-Oca, Incomplete information and risk sensitive analysis of sequential games without a predetermined order of turns
  2. Rolando Cavazos-Cadena, Luis Rodríguez-Gutiérrez, Dulce María Sánchez-Guillermo, Markov stopping games with an absorbing state and total reward criterion
  3. Jaicer López-Rivero, Rolando Cavazos-Cadena, Hugo Cruz-Suárez, Risk-sensitive Markov stopping games with an absorbing state
  4. Manuel A. Torres-Gomar, Rolando Cavazos-Cadena, Hugo Cruz-Suárez, Denumerable Markov stopping games with risk-sensitive total reward criterion

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