We give a short new proof of the existence of optimal solutions to a continuous time formulation of the two-armed bandit problem, using a new topological embedding of the set of randomized optional increasing paths. We do not make any hypothesis on the two-parameter filtration, other than completeness and right-continuity.
@article{1176990946,
author = {Dalang, Robert C.},
title = {Randomization in the Two-Armed Bandit Problem},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 218-225},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990946}
}
Dalang, Robert C. Randomization in the Two-Armed Bandit Problem. Ann. Probab., Tome 18 (1990) no. 4, pp. 218-225. http://gdmltest.u-ga.fr/item/1176990946/