Is real-valued minimax pathological?

  • Authors:

  • Mitja Luštrek;Matjaž Gams;Ivan Bratko

  • Affiliations:

  • Department of Intelligent Systems, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia;Department of Intelligent Systems, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia;Faculty of Computer and Information Science, University of Ljubljana, Tržaška cesta 25, 1000 Ljubljana, Slovenia

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2006

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Abstract

Deeper searches in game-playing programs relying on the minimax principle generally produce better results. Theoretical analyses, however, suggest that in many cases minimaxing amplifies the noise introduced by the heuristic function used to evaluate the leaves of the game tree, leading to what is known as pathological behavior, where deeper searches produce worse results. In most minimax models analyzed in previous research, positions' true values and sometimes also heuristic values were only losses and wins. In contrast to this, a model is proposed in this paper that uses real numbers for both true and heuristic values. This model did not behave pathologically in the experiments performed. The mechanism that causes deeper searches to produce better evaluations is explained. A comparison with chess is made, indicating that the model realistically reflects position evaluations in chess-playing programs. Conditions under which the pathology might appear in a real-value model are also examined. The essential difference between our real-value model and the common two-value model, which causes the pathology in the two-value model, is identified. Most previous research reports that the pathology tends to disappear when there are dependences between the values of sibling nodes in a game tree. In this paper, another explanation is presented which indicates that in the two-value models the error of the heuristic evaluation was not modeled realistically.