一个比Alpha-beta更好的Minimax算法？否和是
A Minimax Algorithm Better Than Alpha-beta?: No and Yes
摘要：
本文对我们理解固定深度极大极小搜索有三个主要贡献：（A）基于Alpha-Beta，提出了Stockman的SSS * 算法的一个新公式。它解决了SSS * 的所有已知缺点，最终将其转化为实用算法。实际上，我们证明了SSS *= α-β +转换表。关键的一步是认识到换位表包含所谓的解树，这种结构用于像SSS * 这样的最佳优先搜索算法。在创建了一个实用的版本，我们提出了三个不同的极大极小游戏的比赛游戏程序的性能测量，产生的结果，矛盾的一些出版物。(B)基于我们在理解SSS * 的尝试中获得的见解，我们提出了一个框架，该框架有助于构建几个最佳优先的固定深度游戏树搜索算法，已知的和新的。该框架基于深度优先空窗口Alpha-Beta搜索，并通过存储进行了增强，以允许对以前的搜索结果进行改进。它将注意力集中在算法之间的本质区别上。(C)我们提出了一个新的框架，MTD（f）。它非常适合与迭代深化一起使用，并且比目前大多数最先进的游戏程序中使用的算法性能更好。我们提供了实验证据来解释为什么MTD（f）比其他固定深度的minimax算法性能更好。
英文摘要：
This paper has three main contributions to our understanding of fixed-depth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS*, finally transforming it into a practical algorithm. In effect, we show that SSS* = alpha-beta + ransposition tables. The crucial step is the realization that transposition tables contain so-called solution trees, structures that are used in best-first search algorithms like SSS*. Having created a practical version, we present performance measurements with tournament game-playing programs for three different minimax games, yielding results that contradict a number of publications. (B) Based on the insights gained in our attempts at understanding SSS*, we present a framework that facilitates the construction of several best-first fixed- depth game-tree search algorithms, known and new. The framework is based on depth-first null-window Alpha-Beta search, enhanced with storage to allow for the refining of previous search results. It focuses attention on the essential differences between algorithms. (C) We present a new instance of the framework, MTD(f). It is well-suited for use with iterative deepening, and performs better than algorithms that are currently used in most state-of-the-art game-playing programs. We provide experimental evidence to explain why MTD(f) performs better than the other fixed-depth minimax algorithms.
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。
