Randomized and Relaxed Strategies in Continuous-Time Markov Decision Processes
Randomized and Relaxed Strategies in Continuous-Time Markov Decision Processes
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DOI：
10.1137/15m1014012
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发表时间：
2015-12
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影响因子：
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通讯作者：
A. Piunovskiy
中科院分区：
文献类型：
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作者：
A. Piunovskiy
本文的目标之一是描述一个广泛的控制策略，其中包括传统的放松策略，以及所谓的随机策略，出现在半马尔可夫决策过程的框架。如果目标是跳跃累积的总期望成本，则不失一般性，可以只考虑马尔可夫松弛策略。在一个简单的条件下，马尔可夫随机化策略也是充分的。通过实例说明了上述条件的重要性。最后，在没有任何条件的情况下，这类所谓的Poisson相关策略在最优化问题中也是充分的。所得结果不仅适用于贴现模型，也适用于长期平均成本模型。
One of the goals of this article is to describe a wide class of control strategies, which includes the traditional relaxed strategies, as well as the so called randomized strategies which appeared earlier only in the framework of semi-Markov decision processes. If the objective is the total expected cost up to the accumulation of jumps, then without loss of generality one can consider only Markov relaxed strategies. Under a simple condition, the Markov randomized strategies are also sufficient. An example shows that the mentioned condition is important. Finally, without any conditions, the class of so called Poisson-related strategies is also sufficient in the optimization problems. All the results are applicable to the discounted model, they may be useful also for the case of long-run average cost.