Displaying similar documents to “Minimizing risk probability for infinite discounted piecewise deterministic Markov decision processes”

Risk probability optimization problem for finite horizon continuous time Markov decision processes with loss rate

Haifeng Huo, Xian Wen (2021)

Kybernetika

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This paper presents a study the risk probability optimality for finite horizon continuous-time Markov decision process with loss rate and unbounded transition rates. Under drift condition, which is slightly weaker than the regular condition, as detailed in existing literature on the risk probability optimality Semi-Markov decision processes, we prove that the value function is the unique solution of the corresponding optimality equation, and demonstrate the existence of a risk probability...

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,...

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...

Identification of optimal policies in Markov decision processes

Karel Sladký (2010)

Kybernetika

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In this note we focus attention on identifying optimal policies and on elimination suboptimal policies minimizing optimality criteria in discrete-time Markov decision processes with finite state space and compact action set. We present unified approach to value iteration algorithms that enables to generate lower and upper bounds on optimal values, as well as on the current policy. Using the modified value iterations it is possible to eliminate suboptimal actions and to identify an optimal...

A stopping rule for discounted Markov decision processes with finite action sets

Raúl Montes-de-Oca, Enrique Lemus-Rodríguez, Daniel Cruz-Suárez (2009)

Kybernetika

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In a Discounted Markov Decision Process (DMDP) with finite action sets the Value Iteration Algorithm, under suitable conditions, leads to an optimal policy in a finite number of steps. Determining an upper bound on the necessary number of steps till gaining convergence is an issue of great theoretical and practical interest as it would provide a computationally feasible stopping rule for value iteration as an algorithm for finding an optimal policy. In this paper we find such a bound...

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...