Displaying similar documents to “Optimal stopping for Markov Processes”

Optimal stopping for Markov Processes

Massimo Lorenzani (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questa nota presentiamo dei nuovi risultati sul problema di tempo d’arresto ottimale per processi di Markov con tempo discreto.

Deterministic optimal policies for Markov control processes with pathwise constraints

Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma (2012)

Applicationes Mathematicae

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This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which...

Risk-sensitive average optimality in Markov decision processes

Karel Sladký (2018)

Kybernetika

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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...

Uniqueness of optimal policies as a generic property of discounted Markov decision processes: Ekeland's variational principle approach

R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca, Enrique Lemus-Rodríguez (2016)

Kybernetika

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Many examples in optimization, ranging from Linear Programming to Markov Decision Processes (MDPs), present more than one optimal solution. The study of this non-uniqueness is of great mathematical interest. In this paper the authors show that in a specific family of discounted MDPs, non-uniqueness is a “fragile” property through Ekeland's Principle for each problem with at least two optimal policies; a perturbed model is produced with a unique optimal policy. This result not only supersedes...

Mean-variance optimality for semi-Markov decision processes under first passage criteria

Xiangxiang Huang, Yonghui Huang (2017)

Kybernetika

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This paper deals with a first passage mean-variance problem for semi-Markov decision processes in Borel spaces. The goal is to minimize the variance of a total discounted reward up to the system's first entry to some target set, where the optimization is over a class of policies with a prescribed expected first passage reward. The reward rates are assumed to be possibly unbounded, while the discount factor may vary with states of the system and controls. We first develop some suitable...

Another set of verifiable conditions for average Markov decision processes with Borel spaces

Xiaolong Zou, Xianping Guo (2015)

Kybernetika

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In this paper we give a new set of verifiable conditions for the existence of average optimal stationary policies in discrete-time Markov decision processes with Borel spaces and unbounded reward/cost functions. More precisely, we provide another set of conditions, which only consists of a Lyapunov-type condition and the common continuity-compactness conditions. These conditions are imposed on the primitive data of the model of Markov decision processes and thus easy to verify. We also...

Semi-Markov control processes with non-compact action spaces and discontinuous costs

Anna Jaśkiewicz (2009)

Applicationes Mathematicae

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We establish the average cost optimality equation and show the existence of an (ε-)optimal stationary policy for semi-Markov control processes without compactness and continuity assumptions. The only condition we impose on the model is the V-geometric ergodicity of the embedded Markov chain governed by a stationary policy.

Average cost Markov control processes with weighted norms: existence of canonical policies

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.

First passage risk probability optimality for continuous time Markov decision processes

Haifeng Huo, Xian Wen (2019)

Kybernetika

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In this paper, we study continuous time Markov decision processes (CTMDPs) with a denumerable state space, a Borel action space, unbounded transition rates and nonnegative reward function. The optimality criterion to be considered is the first passage risk probability criterion. To ensure the non-explosion of the state processes, we first introduce a so-called drift condition, which is weaker than the well known regular condition for semi-Markov decision processes (SMDPs). Furthermore,...