Contemporary Mathematics
Volume 1211, 1992
Optimal Selection, Learning and Machine
ABSTRACT. One aspect of human intelligence is the ability to select spe-
cific objectives converging to a global goal. New technologies indicate a
need for similar characteristics in machine intelligence. There are situar-
tions where the lack of prior information about the random environment
which a machine will meet does not allow one to program a precise objec-
tive. We then want the machine to interpret vaguely defined objectives in
the present environment as specific objectives and to control the currently
chosen objective on-line.
This paper proposes some steps to an implementation of such a type of
machine intelligence. The approach is based on optimal selection models.
We first compare the tractability of different sequential selection models
for this purpose. Our approach is then built on the continuous arrival time
model with an unknown number of options. The simple idea consists of
a history-driven selection of varying objective functions for which memo-
rized optimal cutoff-times strategies can be applied after a suitable time
1980 Mathematics Subject Classification (1985 Revision). Primary 60G12; secondary
60Gl4, 60G40.
Key words and phrases. Unknown number of options, rank-based strategies, cutoff-times,
top-percentage selection, vaguely defined objectives, time-transformation, history-driven selec-
tion of objectives, "Turing test".
The research leading to this paper, written at the University of Arizona, Tucson, and the
University of California, Los Angeles, was supported by the Stimulation Action for Scientific
Research of the European Communities through the project "Automatic Decision Strategies"
(#ST2J-0277-C), and by the Alexander von Humboldt Foundation. It is also my pleasure
to thank here my former students at F. U. Notre-Dame de Ia Paix, Namur: H. Mahiat, M.
Pierard, X. Rutten, and E. Simonis, for their computational help and nice simulation programs.
My particular thanks go to T.S. Ferguson for his many comments and fruitful suggestions to
improve the paper.
This paper is in final form and no version of it will be submitted for publication elsewhere.
1992 American Mathematical Society
0271-4132/92 Sl.OO
$.25 per page
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