Using Forward Induction to Evaluate Sequential Allocation Procedures

Janis Hardwick
Statistics Department, University of Michigan

Quentin F. Stout
EECS Department, University of Michigan

Abstract: Forward induction is a technique to speed the process of making multiple exact evaluations of a sequential allocation procedure, where the options are discrete and their outcomes follow a discrete distribution. Multiple evaluations are needed for determining criteria such as maxima or minima over regions (where the location of the extremal value is unknown in advance), for visualizing characteristics such as robustness, or for obtaining the distribution of a statistic rather than just its mean. By using an initial phase to determine the number of paths reaching each terminal state, the subsequent evaluations are far faster than repeated use of backward induction. Algorithms are given for fully sequential and staged sequential procedures, and the procedures can be either deterministic or random. The procedures can be generated by any technique (including dynamic programming), and the evaluations performed can be quite flexible and need not be related to the method of obtaining the procedure. While the emphasis is on forward induction, the techniques used to speed up the analyses of staged allocation procedures can also be used to improve backward induction for such procedures. If multiple evaluations need to be carried out, however, forward induction will still be far superior.

Keywords: backward induction, adaptive allocation, staged allocation, path counting, Bayesian, bandit problems

AMS Classifications: 62L10, 90C35, 68Q25, 62A15

Full paper (in compressed Postscript)

Copyright © 1997, 1996. Last modified: 5 Mar 1997