On Optimal Game-Tree Search using Rational Meta-Reasoning

In this paper we outline a general approach to the study of problem-solving, in which search steps are considered decisions in the same sense as actions in the world. Unlike other metrics in the l i terature, the value of a search step is defined as a real u t i l i t y rather than as a quasiut i l i ty , and can therefore be computed directly f rom a model of the base-level problem-solver. We develop a formula for the expected value of a search step in a game-playing context using the single-step assumption, namely that a computation step can be evaluated as it was the last to be taken. We prove some metalevel theorems that enable the development of a low-overhead algori thm, MGSS*, that chooses search steps in order of highest estimated ut i l i ty. Al though we show that the single-step assumption is untenable in general, a program implemented for the game of Othello soundly beats an alpha-beta search while expanding signif icantly fewer nodes, even though both programs use the same evaluation function.