Multiple Objective Nonatomic Markov Decision Processes with Total Reward Criteria
Multiple Objective Nonatomic Markov Decision Processes with Total Reward Criteria
复制标题
具有总奖励标准的多目标非原子马尔可夫决策过程
DOI：
10.1006/jmaa.2000.6819
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发表时间：
2000
影响因子：
1.3
通讯作者：
A. B. Piunovskiy
中科院分区：
文献类型：
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作者：
E. Feinberg;A. B. Piunovskiy
我们考虑一个具有不可数状态空间和多重奖励的马尔可夫决策过程。对于每个策略，其性能由总期望奖励的向量来评估。在标准连续性假设和所有初始概率和转移概率都是非原子的附加假设下，证明了所有策略的性能向量集等于（非随机）马尔可夫策略的性能向量集。这一结果表明，对于具有总奖励的非原子约束马尔可夫决策过程，存在最优（非随机）马尔可夫策略。我们提供了两个应用我们的结果约束多目标问题的例子，在库存控制和财务。
We consider a Markov decision process with an uncountable state space and multiple rewards. For each policy, its performance is evaluated by a vector of total expected rewards. Under the standard continuity assumptions and the additional assumption that all initial and transition probabilities are nonatomic, we prove that the set of performance vectors for all policies is equal to the set of performance vectors for (nonrandomized) Markov policies. This result implies the existence of optimal (nonrandomized) Markov policies for nonatomic constrained Markov decision processes with total rewards. We provide two examples of applications of our results to constrained multiple objective problems in inventory control and finance.