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Studios on theory of optimization with utility in stochastic model

随机模型效用优化理论工作室

基本信息

批准号：
14540125
负责人：
OHTSUBO Yoshio
金额：
$ 2.18万
依托单位：
Kochi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540125/
关键词：
Markov decision process threshold probability optimal value and optimal policy equivalence class Fuzzy measure stochastic optimization finite intersection family EM algorithm ファジィ測度確率モデル最適化理論最適停止問題ファジィ決定過程動的計画スターリングの公式

项目摘要

The summary of research results is as follows.1.We consider risk minimizing problems in undiscounted Markov decisions processes with a target set. We formulate the problem as an infinite horizon case with a recurrent class. We show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy. Also we give several value iteration methods and a policy improvement method. We also consider eight problems in which we maximize or minimize threshold probabilities in discounted Markov decision processes with bounded reward set. We show that such problems are classified to two equivalence classes and give a relationship between optimal values and optimal policies of problems in each equivalence class. We also give two sufficient conditions for the existence of an optimal policy. Finally we give a relationship of optimal values between first and second equivalence classes.2.We solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming. The basic idea is to apply invariant imbedding method for stochastic programming.3.We show that weakly null-additive fuzzy measures on metric spaces posses regularity Lusin's theorem is generalized to fuzzy measure space by using the regularity and weakly null-additivity4.We introduce an idea of finite intersection family into a topological space, characterize several concepts in a topological space by mean of finite intersection family and illustrate some applications of finite intersection family.5.EM-algorithm users believe that the conditions of Wu(1983) assure the convergence of GEM sequence, but this paper gives a brief counter example which satisfies Wu's conditions but not converge to MILE or any optimal solutions. It also gives a correction of his proof for the convergence of EM sequence.

主要研究结果如下：1.考虑了目标集为非折扣马氏决策过程的风险最小化问题。我们制定的问题作为一个无限的地平线的情况下，经常性的类。我们证明了最优值函数是最优性方程的唯一解，并且存在平稳最优策略。给出了几种数值迭代方法和一种策略改进方法。我们还考虑了八个问题，其中我们最大化或最小化的阈值概率折扣马尔可夫决策过程有界的回报集。我们证明了此类问题可分为两个等价类，并给出了每个等价类中问题的最优值和最优策略之间的关系。我们还给出了最优策略存在的两个充分条件。最后给出了第一等价类和第二等价类之间的最优值关系。2.利用动态规划方法求解了一个具有前向递归准则的有限时间随机优化问题。3.证明了度量空间上的弱零可加模糊测度的正则性，利用正则性和弱零可加性将Lusin定理推广到模糊测度空间。4.在拓扑空间中引入有限交族的概念，利用有限交族刻画了拓扑空间中的几个概念，并举例说明了有限交族的一些应用。本文给出了一个简单的反例，它满足吴的条件，但不收敛于MILE或任何最优解。对他关于EM序列收敛性的证明进行了修正。