Scalable Algorithms for Adaptive Statistical Designs

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.

Algorithms for response adaptive sampling designs

“…By linearizing the index scheme the memory required can be reduced to the number of states. See Ohemke et al3 for this and other time and space optimizations for serial and parallel programs. Using these optimizations, it is currently possible to optimize the two‐armed Bernoulli bandit problem for experimental sizes of many hundreds on a laptop computer, and the three‐armed bandit for many hundreds on a parallel computer.…”