Search+Pathology

toc =Decision vs Evaluation= Independently, pathology in game trees was coined by Dana Nau, who discovered pathology to exist in a large class of games under the assumption of independence of sibling values of trees with low branching factor (i.e. binary trees) with game theoretic leaf values of win and loss {1, -1}. In a simulation, Nau introduced strong dependencies between sibling nodes and discovered that this can cause search-depth pathology to disappear. While Nau was primarily concerned with decision accuracy, Beal, as well as Bratko and Gams were concerned with evaluation accuracy.  =Random Evaluations= Quite contrary to pathology in chess, Beal and others demonstrated, that deeper search with random leaf values yields to better play. As a quintessence, Dana Nau et al. suggested an //Error minimizing minimax search// in their recent paper.
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 * [[image:Membranous_nephropathy_-_mpas_-_very_high_mag.jpg link="https://en.wikipedia.org/wiki/File:Membranous_nephropathy_-_mpas_-_very_high_mag.jpg"]] ||~  || **Pathology** in game-trees is a counterintuitive phenomenon where a deeper minimax search results in worse play. It was discovered by Don Beal, who constructed a simple mathematical model to analyze the minimax algorithm. To his surprise, the analysis of the model showed that the backed-up values were actually somewhat less trustworthy than the heuristic values themselves. ||
 * Micrograph of membranous nephropathy ||~  ||^   ||

=See also=
 * Conspiracy Numbers
 * Depth
 * Diminishing Returns
 * Score Granularity
 * Search Instability
 * Search with Random Leaf Values
 * Singularity and Pathology

=Publications=

1979

 * Dana Nau (**1979**). //Quality of Decision Versus Depth of Search on Game Trees.// Ph.D. dissertation, Duke University
 * Dana Nau (**1979**). //Preliminary results regarding quality of play versus depth of search in game playing.// First Internat. Symposium on Policy Analysis and Information Systems, pp. 210–217, [|pdf]

1980 ...

 * Don Beal (**1980**). //An analysis of minimax//. Advances in Computer Chess 2
 * Dana Nau (**1980**). //Pathology on game trees: A summary of results.// In Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 102–104, [|pdf]
 * Dana Nau (**1982**). //An Investigation of the Causes of Pathology in Games.// [|Artificial Intelligence], Vol. 19, 257–278, [|University of Maryland, College Park], Recommended by Judea Pearl, [|pdf]
 * Ivan Bratko, Matjaž Gams (**1982**). //Error Analysis of the Minimax Principle//. Advances in Computer Chess 3
 * Don Beal (**1982**). //Benefits of minimax search//. Advances in Computer Chess 3
 * Dana Nau (**1983**). //Decision quality as a function of search depth on game trees.// Journal of the ACM 30(4):687–708, [|pdf]
 * Dana Nau (**1983**). //Pathology on game trees revisited, and an alternative to minimaxing.// [|Artificial Intelligence], Vol. 21, No. 1-2, Reprinted in Judea Pearl (ed.), Search and Heuristics, North-Holland Publishing Company, Amsterdam, [|pdf]
 * Judea Pearl (**1983**). //On the Nature of Pathology in Game Searching//. [|Artificial Intelligence], Vol. 20, 427-453.

1985 ...

 * Bruce Abramson (**1985**). //A Cure for Pathological Behavior in Games that Use Minimax.// Proceedings of the Workshop on Uncertainty in Artificial Intelligence, 1985, 225-231.
 * Agata Muszycka (**1985**). //Game Trees: Searching Techniques and Pathological Phenomenon//. Master of Computer Science, Department of Computer Science, [|Concordia University], [|Montreal]
 * Bruce Abramson (**1986**). //An Explanation of and Cure for Minimax Pathology.// Uncertainty in Artificial Intelligence, Laveen Kanal and John Lemmer, eds. (Amsterdam: North Holland, 1986), 495-504.
 * Günther Schrüfer (**1986**). //Presence and Absence of Pathology on Game Trees//. Advances in Computer Chess 4
 * Ingo Althöfer (**1988**). //Root Evaluation Errors: How they Arise and Propagate//. ICCA Journal, Vol. 11, Nos. 2/3
 * Liwu Li (**1989**). //[|Probabilistic Analysis of Search]//. Ph.D. thesis, University of Alberta, advisor Tony Marsland

1990 ...

 * Liwu Li, Tony Marsland (**1990**). //On Minimax Game Tree Search Pathology and Node-value Dependence//. TR90-24, University of Alberta, [|pdf]
 * Ingo Althöfer (**1991**). //On Pathology in Game Tree and other Recursion Tree Models//, Habilitation Thesis (June 1991), Faculty of Mathematics, [|University of Bielefeld]
 * Don Beal, Martin C. Smith (**1994**). //Random Evaluations in Chess//. ICCA Journal, Vol. 17, No. 1
 * Don Beal, Martin C. Smith (**1994**). //Random Evaluations in Chess//. Advances in Computer Chess 7

1995 ...

 * Mark Levene, Trevor Fenner (**1995**). //A Partial Analysis of Minimaxing Game Trees with Random Leaf Values//. ICCA Journal, Vol. 18, No. 1
 * Ingo Althöfer, Imre Leader (**1995**). //[|Correlation of Boolean Functions and Pathology in Recursion Trees]//. [|SIAM Journal on Discrete Mathematics], Vol. 8, No. 4
 * Don Beal (**1999**). //The Nature of MINIMAX Search//. Ph.D. thesis, IKAT, ISBN 90-62-16-6348

2000 ...

 * Mark Levene, Trevor Fenner (**2001**). //The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values//. [|Artificial Intelligence], Vol. 130, No. 1, Review in ICGA Journal, Vol. 24, No. 4

2005 ...

 * Mitja Luštrek, Matjaž Gams, Ivan Bratko (**2005**). //[|Why Minimax Works: An Alternative Explanation]//. [|IJCAI 2005]
 * Aleksander Sadikov, Ivan Bratko, Igor Kononenko (**2005**). //[|Bias and Pathology in Minimax Search]//. [|Theoretical Computer Science],, Vol. 349, 2, [|pdf]
 * Mitja Luštrek, Matjaž Gams, Ivan Bratko (**2006**). //Is Real-Valued Minimax Pathological//? [|Artificial Intelligence], Vol. 170, [|pdf]
 * Brandon Wilson, Austin Parker, Dana Nau (**2009**). //Error Minimizing Minimax: Avoiding Search Pathology in Game Trees//. [|pdf]

2010 ...

 * Dana S. Nau, Mitja Luštrek, Austin Parker, Ivan Bratko, Matjaž Gams (**2010**). //[|When is it better not to look ahead?]//. [|Artificial Intelligence], Vol. 174, No. 16–17, [|preprint as pdf]
 * Mitja Luštrek, Ivan Bratko, Matjaž Gams (**2011**). //[|Independent-valued minimax : Pathological or beneficial?]// [|Theoretical Computer Science], Vol. 422, [|pdf]

=Forum Posts= > [|Re: Null Move in Quiescent search] by Marcel van Kervinck, CCC, December 10, 2015 » PDS > [|Re: Null Move in Quiescent search] by Harm Geert Muller, CCC, December 12, 2015
 * [|Pathology on Game trees] by Gerd Isenberg, CCC, July 22, 2010
 * [|Re: Null Move in Quiescent search] by Harm Geert Muller, CCC, December 10, 2015 » Null Move Pruning, Quiescence Search
 * [|random evaluation perturbation factor] by Stuart Cracraft, CCC, April 24, 2017

=External Links= > media type="custom" key="24354636"
 * [|Pathology (disambiguation) from Wikipedia]
 * [|Pathological (mathematics) from Wikipedia]
 * [|Pathology from Wikipedia]
 * [|Pathological science from Wikipedia]
 * [|Yuja Wang] improvises on [|Saint-Saëns]/[|Liszt]/[|Horowitz], [|Danse Macabre], [|YouTube] Video

=References= =What links here?= include page="Search Pathology" component="backlinks" limit="80"
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