Growth Optimality for Branching Markov Decision Chains
Growth Optimality for Branching Markov Decision Chains
复制标题
分支马尔可夫决策链的增长最优性
DOI：
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复制
发表时间：
1982
影响因子：
1.7
通讯作者：
P. Whittle
中科院分区：
文献类型：
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作者：
U. Rothblum;P. Whittle
本文考虑一个称为分支马尔可夫决策链的（乘法）过程，其中第N个周期结束时的输出等于在周期1，...，N开始时分别选择的N个非负矩阵的乘积，乘以一个正的（固定的）终端奖励向量。假设上述转移矩阵是从以乘积形式给出的矩阵的有限集合（即，可以从非负行向量的有限集合中独立地选择矩阵的行）。对于每个坐标s，我们分别定义输出流的sth坐标的几何和代数增长率。这些增长率被定义为使得相应序列的量级为αNNk，其中α是几何增长率，k是代数增长率。本文的主要结果是建设性地建立存在的过渡矩阵，其重复使用将保证，为每个坐标，实现最佳的几何形状。
This paper considers a (multiplicative) process called branching Markov decision chains in which the output at the end of the Nth period equals the product of N nonnegative matrices chosen at the beginning of periods 1, …, N, respectively, times a positive (fixed) terminal reward vector. It is assumed that the above transition matrices are drawn out of a finite set of matrices given in product form (i.e., the rows of the matrices can be selected independently out of finite sets of nonnegative row vectors). For each coordinate s we define the geometric and algebraic growth rates, respectively, of the sth coordinate of the stream of output. These growth rates are defined so that the magnitude of the corresponding sequence is of the order αNNk where α is the geometric growth rate and k is the algebraic growth rate. The main result of this paper is the constructive establishment of the existence of a transition matrix whose repeated use will guarantee, for each coordinate, the achievement of the best geometri...