This research will study sequential decision problems called the bandit problems. At each stage of a sequence of trials the experimenter has a choice of actions. The outcomes of the choices have a certain amount of randomness. The experimenter has two conflicting aims; to achieve immediate success and to acquire information useful for making future choices of actions. The research will focus on experimental strategies that are good even when there is little initial information concerning the merits of the various actions. This research will also study probabilistic combinatorics. It will consider counting the number of specific objects in some collection when the objects are chosen at random on an equiprobable basis. For example, a ramdom listing of n numbers may be chosen and the number of times a larger number immediately precedes a smaller number may be studied. Behavior of such probability distributions for large number of objects will be studied for a variety of combinatorial settings.
