A program for sequential allocation of three Bernoulli populations
A program for optimizing and analyzing sequential allocation problems involving three Bernoulli populations and a general objective function is described. Previous researchers had considered this problem computationally intractable, and there appears to be no prior exact optimizations for such problems, even for very small sample sizes. This paper contains a description of the program, along with the techniques used to scale it to large sample sizes. The program currently handles problems of size 200 or more by using a modest parallel computer, and problems of size 100 on a workstation. As an illustration, the program is used to create an adaptive sampling procedure that is the optimal solution to a 3-arm bandit problem. The bandit procedure is then compared to two other allocation procedures along various Bayesian and frequentist metrics. Extensions enabling the program to solve a variety of related problems are discussed.
parallel computing sequential sampling multi-arm bandit dynamic programming adaptive allocation clinical trial load balancing high-performance computing recursive equations design of experiments