A CLASS OF SEQUENTIAL SAMPLING PROBLEMS ARISING IN CERTAIN LEARNING SITUATIONS.
Abstract
A strategist is to decide on each of n turns whether to take a sample from a certain fixed random variable, and receive the outcome as payoff, or to receive as payoff the largest value of the random variable he has discovered so far. The expected total payoff for the n turns is to be maximized. It is shown that the following decision procedure is the solution. x prime is the current record value, and F(x) is the distribution function of the random variable. A strategy for an indefinite number of turns is described, and for suitable distributions it is shown that the limit of the ratio of the payoff accumulated by this strategy in n turns to the payoff accumulated by the optimal strategy for n turns in one, with probability one. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0664144
Entities
People
- Edwin Bainbridge
Organizations
- University of Michigan