pgamePathology - Error Minimizing Minimax: Avoiding Search...

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Unformatted text preview: Error Minimizing Minimax: Avoiding Search Pathology in Game Trees Brandon Wilson 1 and Austin Parker 2 and Dana Nau 1 , 3 , 2 1 Dept. of Computer Science, 2 Institute for Advanced Computer Studies, and 3 Institute for Systems Research University of Maryland College Park, Maryland 20742, USA email: { bswilson,austinjp,nau } @cs.umd.edu Abstract Game-tree pathology is a phenomenon where deeper mini- max search results in worse play. It was was discovered 30 years ago (Nau 1982) and shown to exist in a large class of games. Most games of interest are not pathological so there has been little research into searching pathological trees. In this paper we show that even in non-pathological games, there likely are pathological subtrees. Further, we introduce er- ror minimizing minimax search, an adaptation of minimax that recognizes pathological subtrees in arbitrary games, and cuts off search accordingly (shallower search is more effec- tive than deeper search in pathological subtrees). Finally, we present experimental studies of error minimizing mini- max in two different games. In our experiments, error mini- mizing minimax outperformed minimax, sometimes substan- tially, and never exhibited pathological characteristics. Introduction Game-tree search pathology is a phenomenon where deeper minimax search leads to more erroneous decision-making. In a pathological game tree, an algorithm minimaxing to depth 9 will make worse decisions than an algorithm min- imaxing to depth 5 (so long as the game ends in more than 9 moves). To those familiar with computational game play- ing, this is a strange result. Conventional wisdom states that deeper search produces better play – this has cer- tainly been the case for chess. However, there is a large class of games that exhibit pathology, and a large body of work trying to understand why and what kinds of game trees are pathological (Nau 1982; Bratko and Gams 1982; Sadikov, Bratko, and Kononenko 2005; Beal 1980; Pearl 1984). In this paper, we show how local pathologies can occur at certain kinds of subtrees of a game tree, and how to modify a minimax style search procedure to recognize local patholo- gies. Local pathologies are likely to occur in all interesting games, so we can hypothesize that even in games not known to be pathological, a search procedure that recognizes and accounts for such pathologies should produce better results. We call the search procedure that recognizes and avoids local pathologies error minimizing minimax (EMM) search. EMM search works by tracking both the minimax value of a Copyright c 2009, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. node and the error associated with the node. As the minimax value of a node is aggregated up the tree in a minimax fash- ion, the associated error is also aggregated up the tree in a fashion similar to the product rule from (Tzeng and Purdom 1983). At each node in the search, the static evaluation func-1983)....
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pgamePathology - Error Minimizing Minimax: Avoiding Search...

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