Denumerable state semi-markov decision processes with unbounded costs, average cost criterion : (preprint)
Denumerable state semi-markov decision processes with unbounded costs, average cost criterion : (preprint)
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具有无界成本的可枚举状态半马尔可夫决策过程，平均成本标准：（预印本）
DOI：
10.1016/0304-4149(79)90034-6
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
H. Tijms
中科院分区：
文献类型：
--
作者：
A. Federgruen;A. Hordijk;H. Tijms
本文对状态空间可数、度量行动集紧、一步费用无界的平均费用半马氏决策模型，在其基础马氏链只有一个遍历集的情况下，建立了一个较完整的最优性理论.在一个条件下，粗略地说，需要存在一个有限的集合，使得在所有的平稳政策的期望时间的上确界和总的期望绝对成本，直到第一次返回到这个集合是有限的任何初始状态，我们将验证的有限解的平均成本最优方程和平均成本最优平稳政策的存在。
This paper establishes a rather complete optimality theory for the average cost semi-Markov decision model with a denumerable state space, compact metric action sets and unbounded one-step costs for the case where the underlying Markov chains have a single ergotic set. Under a condition which, roughly speaking, requires the existence of a finite set such that the supremum over all stationary policies of the expected time and the total expected absolute cost incurred until the first return to this set are finite for any starting state, we shall verify the existence of a finite solution to the average costs optimality equation and the existence of an average cost optimal stationary policy.