288 pp. per issue
6 x 9, illustrated
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Neural Computation

January 1, 1999, Vol. 11, No. 1, Pages 215-227
(doi: 10.1162/089976699300016881)
© 1999 Massachusetts Institute of Technology
Propagating Distributions Up Directed Acyclic Graphs
Article PDF (130.26 KB)

In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding on a move after search was completed. In some games, such as chess and Othello, the same position can occur more than once, collapsing the game tree to a directed acyclic graph (DAG). This induces correlations among the distributions at sibling nodes. This article discusses some issues that arise in extending our algorithms to a DAG. We give a simply described algorithm for correctly propagating distributions up a game DAG, taking account of dependencies induced by the DAG structure. This algorithm is exponential time in the worst case. We prove that it is #P complete to propagate distributions up a game DAG correctly. We suggest how our exact propagation algorithm can yield a fast but inexact heuristic.