A note on optimality conditions for continuous-time Markov decisionprocesses with average cost criterion

Xianping Guo; Ke Liu

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A note on optimality conditions for continuous-time Markov decisionprocesses with average cost criterion

机译：关于具有平均成本准则的连续时间马尔可夫决策过程的最优性条件的注记

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This note deals with continuous-time Markov decision processes with a denumerable state space and the average cost criterion. The transition rates are allowed to be unbounded, and the action set is a Borel space. We give a new set of conditions under which the existence of optimal stationary policies is ensured by using the optimality inequality. Our results are illustrated with a controlled queueing model. Moreover, we use an example to show that our conditions do not imply the existence of a solution to the optimality equations in the previous literature

机译：本说明涉及具有可数状态空间和平均成本准则的连续时间Markov决策过程。过渡速率是不受限制的，并且动作集是Borel空间。我们给出了一组新的条件，在这些条件下，通过使用最优性不平等来确保最优平稳策略的存在。我们的结果通过受控排队模型进行说明。此外，我们使用一个例子来说明我们的条件并不意味着存在先前文献中最优方程的解。

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《IEEE Transactions on Automatic Control》 |2001年第12期|p.1984-1989|共6页
作者
Xianping Guo; Ke Liu;
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正文语种 eng
中图分类自动化系统;
关键词
Markov processes; decision theory; optimal control; queueing theory; Borel space; action set; average cost criterion; continuous-time Markov decision processes; controlled queueing model; denumerable state space; optimal control; optimality conditions; unbounded tra;

机译：马尔可夫过程;决策理论;最优控制;排队论;桶空间;动作集;平均成本准则;连续时间马尔可夫决策过程;受控排队模型;可缩减状态空间;最优控制;最优性条件;无界通量;

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1. STRONG AVERAGE OPTIMALITY CRITERION FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES [J] . Qingda Wei, Xian Chen Kybernetika . 2014,第6期

机译：连续时间马尔可夫决策过程的强平均最优准则
2. Strong average optimality criterion for continuous-time Markov decision processes [J] . Chen Xian, Wei Qingda Kybernetika . 2014,第6期

机译：连续时间马尔可夫决策过程的强平均最优准则
3. Average cost criterion induced by the regular utility function for continuous-time Markov decision processes [J] . Wei Qingda, Chen Xian Discrete event dynamic systems: Theory and applications . 2017,第3期

机译：连续时间马尔可夫决策过程的常规实用程序函数引起的平均成本标准
4. Denumerable controlled Markov chains with strong average optimality criterion: bounded and unbounded costs [C] . Cavazos-Cadena, R., Fernandez-Gaucherand, . 1994

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5. Controlled Markov chains with risk-sensitive average cost criterion. [D] . Brau Rojas, Agustin. 1999

机译：具有风险敏感平均成本准则的受控马尔可夫链。
6. SIMULATION FROM ENDPOINT-CONDITIONED CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE WITH APPLICATIONS TO MOLECULAR EVOLUTION [O] . Asger Hobolth, Eric A. Stone -1

机译：动态模拟端点空调连续时间的马尔可夫链在有限状态空间应用程序分子进化
7. Strong average optimality criterion for continuous-time Markov decision processes [O] . Wei, Qingda, Chen, Xian 2014

机译：连续时间马尔可夫决策过程的强平均最优准则
8. Denumerables State Semi-Markov Decision Processes with Unbounded Costs, Average Cost Criterion [R] . Federgruen, A., Hordijk, A., Tijms, H. C. 1978

机译：具有无界成本，平均成本准则的可量化状态半马尔可夫决策过程

A note on optimality conditions for continuous-time Markov decisionprocesses with average cost criterion

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