Michael Buro

Improving heurisitic mini-max search by supervised learning

This article surveys three techniques for enhancing heuristic game-tree search pioneered in the authors Othello program LOGISTELLO, which dominated the computer Othello scene for several years and won against the human World-champion 6-0 in 1997. First, a generalized linear evaluation model (GLEM) is described that combines conjunctions of Boolean features linearly. This approach allows an automatic, data driven exploration of the feature space. Combined with efficient least squares weight fitting, GLEM greatly eases the programmers task of finding significant features and assigning weights to them. Second, the selective search heuristic PROBCUT and its enhancements are discussed. Based on evaluation correlations PROBCUT can prune probably irrelevant sub-trees with a prescribed confidence. Tournament results indicate a considerable playing strength improvement compared to full-width a-b search. Third, an opening book framework is presented that enables programs to improve upon previous play and to explore new opening lines by constructing and searching a game-tree based on evaluations of played variations. These general methods represent the state-of-the-art in computer Othello programming and begin to attract researchers in related fields. Copyright 2002 Elsevier Science B.V.

Statistical feature combination for the evaluation of game positions

This article describes an application of three well-known statistical methods in the field of game-tree search: using a large number of classified Othello positions, feature weights for evaluation functions with a game-phase-independent meaning are estimated by means of logistic regression, Fishers linear discriminant, and the quadratic discriminant function for normally distributed features. Thereafter, the playing strengths are compared by means of tournaments between the resulting versions of a world-class Othello program. In this application, logistic regression -- which is used here for the first time in the context of game playing - leads to better results than the other approaches.

On resolution with short clauses

AbstractWe investigate properties ofk-resolution, a restricted version of resolution in which one parent clause must have length at mostk. Starting from a unit-preference strategy, we compare minimal proof lengths of unit-resolution and unrestricted resolution. In particular, we show that the speed-up by using resolution is bound byn

Toward Opening Book Learning

sqrt t

Toward opening book learning

n if the shortest unit-resolution refutation needst steps. Next we present an algorithm which decides whether the empty clause can be deduced by 2-resolution from a formula Φ and has time complexity O(length(Φ)4). Finally we describe effects onk-resolution if a formula is transformed intot-CNF and show that extended 3-resolution is complete and sound.