Bulletin of Mathematical Statistics最新文献_第3页

INFORMATION THEORETICAL APPROACHES IN GAME THEORY 博弈论中的信息理论方法

Bulletin of Mathematical Statistics Pub Date : 1979-03-01 DOI: 10.5109/13128

Seigo Kanô, Yuichi Kai

引用次数: 1

GENERALIZED HADAMARD'S INEQUALITIES AND THEIR APPLICATIONS TO STATISTICS 广义hadamard不等式及其在统计学中的应用

Bulletin of Mathematical Statistics Pub Date : 1979-03-01 DOI: 10.5109/13129

A. Nishi

引用次数: 4

A TRUNCATED PLAY-THE-WINNER PROCEDURE FOR SELECTING THE BEST OF $ k geqq 3 $ BINOMIAL POPULATION 选择最佳的$ k geq3$二项总体的一种截断的“赌赢”程序

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13121

K. Schriever

引用次数: 4

CONTINUOUS TIME NON-COOPERATIVE $ N $-PERSON MARKOV GAMES 连续时间非合作n人马尔可夫对策

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13126

Kensuke Tanaka, Hisafumi Homma

引用次数: 4

A RANDOM WALK AND ITS LIL IN A BANACH SPACE 巴拿赫空间中的随机漫步及其函数

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13125

M. Chang

引用次数: 0

SEMI-MARKOV DECISION PROCESSES WITH COUNTABLE STATE SPACE AND COMPACT ACTION SPACE 具有可数状态空间和紧致作用空间的半马尔可夫决策过程

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13122

M. Yasuda

引用次数: 6

RATES OF CONVERGENCE IN CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCES 鞅差分中心极限定理的收敛速度

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13119

Yutaka Kato

引用次数: 9

STOCHASTIC GAME MODELS FOR THE DETERMINATION OF THE OPTIMAL CONTINUOUS SAMPLING INSPECTION PLANS 确定最优连续抽样检验方案的随机博弈模型

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13120

T. Sakamoto, M. Kurano

引用次数: 2

THE CALUCULATION OF LIMIT PROBABILITIES FOR MARKOV JUMP PROCESSES 马尔可夫跳变过程极限概率的计算

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13124

M. Yasuda

引用次数: 0

POLICY IMPROVEMENT IN MARKOV DECISION PROCESSES AND MARKOV POTENTIAL THEORY 马尔可夫决策过程与马尔可夫势理论的政策改进

Bulletin of Mathematical Statistics Pub Date : 1978-03-01 DOI: 10.5109/13123

M. Yasuda

{"title":"POLICY IMPROVEMENT IN MARKOV DECISION PROCESSES AND MARKOV POTENTIAL THEORY","authors":"M. Yasuda","doi":"10.5109/13123","DOIUrl":"https://doi.org/10.5109/13123","url":null,"abstract":"A connection between Markov Decision Process (MDP) and Markov potential theory has two sides. One is the potential theoritic development of MDP and the other is the alternative proof of the results in MDP owing to Markov potential theory. Shaufele [12] belongs to the later, but it seems interesting from the standpoint of the mathematical programming to establish the development of MDP by using certain potential notion. Several approaches have been tried. Watanabe [16] interpreted the monotonicity of Howard's iteration [8] in the relation to the a dual problem of Linear Programming. By the property of a potential kernel, Furukawa [6] and Aso and Kimura [1] proved a policy improvement. A formulation of MDP by potential theoretic notion has been tried by Hordijk [7]. In many cases it is restricted to a transient potential theory because its analysis is simpler. In this paper we shall define a new potential in order to serve a general policy improvement. Our aim is to expose theorems which are available to several cases of MDP. By the potential theoretic terms, we can interpret policy improvements of MDP as follows ; The increase of rewards in MDP consists of the potential with a charge of an increment of the policy improvement and a regular function. If it is transient, then the potential is reduced to the ordinary one and the regular function equals zero. Hence this consists with that of Watanabe [16]. The merit of the potential is that it connects the policy improvement with the increment of rewards. We shall consider the following cost criteria of MDP ; (1) discounted case, (2) average case, (3) nearly optimal case and (4) sensitive discounted case. Case (1) and (2) are representitive and discussed by many authors. Especially we list up Howard [7] and Blackwell [2], [3] for (1) and Howard [8] and Derman [4], [5] for (2). Case (3) is due to Blackwell [2]. Extending case (3), case (4) is studied by Miller and Veinott [11] and Veinott [14], [15].","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129355215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0