1 . The point of game tree search is to insulate oneself from errors in the evaluation function. The standard approach is to grow a full width tree as deep as time allows, and then value the tree as if the leaf evaluations were exact. This has been effective in many games because of the computational efficiency of the Alphabeta algorithm. But as Bayesians, we want to know the best way to use the inexact statistical information provided by the leaf evaluator to choose our next move. We add a model of uncertainty to the standard evaluation function. Within such a formal model, there is an optimal tree growth procedure and an optimal method of valuing the tree. We describe how to optimally value the tree within our model, and how to efficiently approximate the optimal tree to search. Our tree growth procedure provably approximates the contribution of each leaf to the utility in the limit where we grow a large tree, taking explicit account of the interactions between expanding different ...
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