决策论的两类判据

ON TWO GROUPS OF CRITERIONS IN DECISION THEORY

本文分两个部份。一、用几何方法统一讨论了风险型的期望效益判据，不定型的Ｌａｐｌａｃｅ等可能性判据、Ｈｕｒｗｉｃｚ乐观判据，ｗａｌｄ悲观判据与Ｓａｖａｇｅ后悔判据，还提出了一个望外判据。二，指出了：后悔判据和望外判据，与其他的判据分属两类不同的最优化问题。前一类所得到的最优解有以下两个特点：１．以策略集合为整体，其子集合为局部，则整体的最优解ａ＊不保证是局部的最优解；即使ａ＊属于所论的局部。２．求最优解时，生成算法与分治算法子均不适用。

There are two parts in the article. Firstly. it uses geometrical method to establish systematically several well known decision criterions including expected profit criterion. Laplace's principle-of-insufficient -reason criterion. Hurwicz's optimism criterion.Wald's pessimism criterion and Savage' s regret criterion. In addition. it suggests a so-called unexpectedness criterion.Secondly.it shows with an numerical example that all those criterions can be divided into two groups.Savage's regrer criterion and the unexpectedness criterion belong to one group. and the others belong to another. The former one has the following two characteristics.(i)Let the strategy set be global and its subsets local. The optimum strateqy a in the global need not be optimun in the local even if a belongs to the local. (ii) For examples. generation algorithm and divide-and-conquor algorithm could not be applied to the criterions mentioned.