Optimal and Nearly Optimal Policies in Markov Decision Chains with Nonnegative Rewards and Risk-Sensitive Expected Total-Reward Criterion

Rolando Cavazos-Cadena () and Raúl Montes- de-Oca ()
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Rolando Cavazos-Cadena: Universidad Autónoma Agraria Antonio Narro, Departamento de Estadística y Cálculo
Raúl Montes- de-Oca: Universidad Autónoma Metropolitana, Departamento de Matemáticas

Chapter Chapter 11 in Markov Processes and Controlled Markov Chains, 2002, pp 189-221 from Springer

Abstract: Abstract This work considers Markov decision processes with discrete state space. Assuming that the decision maker has a non-null constant risk-sensitivity, which leads to grade random rewards via the expectation of an exponential utility function, the performance index of a control policy is the risk-sensitive expected total-reward criterion corresponding to a nonnegative reward function. Within this framework, the existence of optimal and approximately optimal stationary policies in the absolute sense is studied. The main results can be summarised as follows: (i) An optimal stationary policy exists if the state and actions sets are finite, whereas an ε-optimal stationary policy is guaranteed when just the state space is finite. (ii) This latter fact is used to obtain, for the general denumerable state space case, that ε-optimal stationary policies exist if the controller is risk-seeking and the optimal value function is bounded. In contrast with the usual approach, the analysis performed in the paper does not involve the discounted criterion, and is completely based on properties of optimal value function, particularly, on the the strong optimality equation.

Keywords: Utility function; constant risk-sensitivity; Ornstein’s theorem; strong optimality equation; risk-seeking controller (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0265-0_11

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DOI: 10.1007/978-1-4613-0265-0_11

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