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arXiv 1301.6729cs.AI
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定义明确的决策情景

Welldefined Decision Scenarios

Thomas D. Nielsen, Finn Verner Jensen

摘要:

影响图作为一个强大的工具,对称决策问题建模。在求解影响图时,我们为所涉及的决策确定一组策略。决策变量的策略原则上是其过去的函数。然而,过去的一些可能与决策无关,并且出于计算原因,重要的是不要处理策略中的冗余变量。我们表明,目前的方法(如“决策贝叶斯球”算法由Shachter UAI98)不确定相关的过去,我们提出了一个完整的算法。实际上,本文采取了一个更一般的开始:当制定一个决策方案的影响图,一个线性的时间顺序的决策变量是必需的。这个约束确保了决策场景的定义是明确的。然而,决策场景的结构通常会产生条件独立的某些决策,因此没有必要对决策施加线性时间排序。在本文中,我们处理部分影响图,即影响图,只有一个部分时间顺序指定。我们提出了一组必要和充分的条件,以确保部分影响图是定义良好的。这些条件被用来作为一个基础,用于构建一个算法,以确定是否部分影响图是明确的。

英文摘要:

Influence diagrams serve as a powerful tool for modelling symmetric decision problems. When solving an influence diagram we determine a set of strategies for the decisions involved. A strategy for a decision variable is in principle a function over its past. However, some of the past may be irrelevant for the decision, and for computational reasons it is important not to deal with redundant variables in the strategies. We show that current methods (e.g. the "Decision Bayes-ball" algorithm by Shachter UAI98) do not determine the relevant past, and we present a complete algorithm. Actually, this paper takes a more general outset: When formulating a decision scenario as an influence diagram, a linear temporal ordering of the decisions variables is required. This constraint ensures that the decision scenario is welldefined. However, the structure of a decision scenario often yields certain decisions conditionally independent, and it is therefore unnecessary to impose a linear temporal ordering on the decisions. In this paper we deal with partial influence diagrams i.e. influence diagrams with only a partial temporal ordering specified. We present a set of conditions which are necessary and sufficient to ensure that a partial influence diagram is welldefined. These conditions are used as a basis for the construction of an algorithm for determining whether or not a partial influence diagram is welldefined.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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