Propagating distributions up directed acyclic graphs.

Abstract:

: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.

journal_name

Neural Comput

journal_title

Neural computation

authors

Baum EB,Smith WD

doi

10.1162/089976699300016881

subject

Has Abstract

pub_date

1999-01-01 00:00:00

pages

215-27

issue

1

eissn

0899-7667

issn

1530-888X

journal_volume

11

pub_type

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