Author: Ingo Althofer
Date: 04:01:46 12/31/05
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On December 31, 2005 at 04:38:46, Rafael Andrist wrote: >On December 30, 2005 at 13:02:43, Ingo Althofer wrote: >>... in case of linear evaluation functions with lots >>of terms there is always a small subset of the terms >>such that this set with the right parameters is >>almost as good as the full evaluation function. > > Can you state this a bit more precise, please? > As long as it is not clear what you mean by "lots of" and "small" > and "almost as good", your statement says nothing and could be > trivially true, if, for ex. > "small" just means "less or equal". I can assure you that the result is not trivial. Unfortunately I wrote the paper, before the mathematical community developed fully "electronized" publication services. So you have to look at the paper versions: The technical result with complete proofs is given in * I. Althofer. On sparse approximations to randomized strategies and convex combinations. Linear Algebra and Applications 199 (1994), 339-355. The application to linear evaluation functions in chess, go, and other games is described in * I. Althofer. On telescoping linear evaluation functions. ICCA-J , Vol 16 (1993), pp. 91-94 (issue June 1993). Funnily, in this context "Go" seems to be only about 2-3 times more complicated than chess, if I remember correctly. (... where complexity is measured in number of linear terms needed to achieve a certain level of quality) Regards, Ingo Althofer.
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