The problem of choice and the optimal stopping rule for a~sequence of random trials
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 534-537
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Suppose we have to choose an element from a finite set $A$ which consist of $n$ elements. Let $A$ be ordered by quality. We regard our choice as successful if the selected element is one of the best $r$ elements of $A$. Let us enumerate the elements of $A$ in such order as we learn them. After learning at we know the comparative qualities of $a_1,a_2,\dots,a_t$ but we know nothing about the quality of the remaining $n-t$ elements of $A$. While learning $a_t$ we can either accept it (then the choice is made) or reject it (then it will be impossible to return to it). We describe the optimal policy which secures the greatest probability of the successful choice and describe its asymptotical behaviour as $n\to\infty$.
@article{TVP_1966_11_3_a15,
author = {S. M. Gusein-Zade},
title = {The problem of choice and the optimal stopping rule for a~sequence of random trials},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {534--537},
publisher = {mathdoc},
volume = {11},
number = {3},
year = {1966},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a15/}
}
TY - JOUR AU - S. M. Gusein-Zade TI - The problem of choice and the optimal stopping rule for a~sequence of random trials JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1966 SP - 534 EP - 537 VL - 11 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a15/ LA - ru ID - TVP_1966_11_3_a15 ER -
S. M. Gusein-Zade. The problem of choice and the optimal stopping rule for a~sequence of random trials. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 534-537. http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a15/