Quentin F. Stout
University of Michigan
Abstract: We present a scalable, high-performance solution to multidimensional recurrences that arise in adaptive statistical designs. Adaptive designs are an important class of learning algorithms for a stochastic environment, and we focus on the problem of optimally assigning patients to treatments in clinical trials. While adaptive designs have significant ethical and cost advantages, they are rarely utilized because of the complexity of optimizing and analyzing them. Computational challenges include massive memory requirements, few calculations per memory access, and multiply-nested loops with dynamic indices.
We analyze the effects of various parallelization options, and while standard approaches do not work well, with effort an efficient, highly scalable program can be developed. This allows us to solve problems 2000 times more complex than had been solved previously. This allows one to address more useful situations, helping make adaptive designs more practical. Further, our work applies to many other problems involving neighbor recurrences, such as generalized string matching.
Our primary example program involves allocating among 3 Bernoulli treatment options. Mathematically, this is modeled as a 3-arm bandit. We develop efficient serial and parallel implementations, with parallel versions for both distributed and shared memory systems. We also analyze a program for allocating among 2 Bernoulli options, where now the responses are delayed. The response delays mean the some patient treatment decisions must be made even though the results of prior patients are still unknown. This greatly complicates the modeling, and new programming challenges occur.
Keywords: adaptive sampling, statistical computing, sequential allocation, multi-arm bandit problem, dynamic programming, backward induction, design of experiments, active learning, stochastic optimization, parallel computing, supercomputing, machine learning, parallel algorithms, controlled clinical trial, high-performance computing, neighbor recurrence equations, delayed response
Complete paper. This paper appears in Scientific Programming 8 (2000), pp. 183-193. It is a corrected reprint of an article first appearing in Proceedings SC 2000 (Supercomputing), 15 p., where it was a finalist for Best Paper.
A preliminary version of this work involving a less scalable implementation appeared in J. Hardwick, R. Oehmke, and Q.F. Stout, "A parallel program for 3-arm bandits", Computing Science and Statistics 29 (1997), pp. 390-395.
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