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 thousands of times more complex than those solved previously, which helps make adaptive designs practical. Further, our work applies to many other problems involving neighbor recurrences, such as generalized string matching.
Highlights
Standard statistical designs define all sampling decisions in advance
In a clinical trial, the number of patients that will receive each treatment is decided before the trial begins
Allocating patients to treatment options so as to optimize their outcomes in a clinical trial can be modeled as a Bayesian bandit problem [2]
Summary
Standard statistical designs define all sampling decisions in advance. In particular, in a clinical trial, the number of patients that will receive each treatment is decided before the trial begins. We primarily report on one case, optimizing an n-stage trial with three treatment options having Bernoulli outcomes This problem is translated into a 6-dimensional dynamic program for which we developed a highly scalable solution, allowing us to create designs of useful size. Neighbor recurrences are quite common, such as the Fibonacci sequence F (n) = F (n − 1) + F (n − 2) or in the use of dynamic programming to solve optimization problems such as the alignment of gene or protein structures in bioinformatics. They occur in backwards induction and path induction [7]. Rerunning the same problem showed very little timing variation, so we merely report average time (see, Section 4.3)
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