Optimal Bayes procedures for selecting the better of two Bernoulli populations

Kulkarni, Radhika V.; Kulkarni, Vidyadhar G.

doi:10.1016/0378-3758(86)90106-0

“…Using only 16 processors of an IBM SP2 we solved the 3-arm, n = 200 problem. This is approximately 500,000 times harder than the problem called "impractical" in [9], and 2,000 times harder than that solved in [3] on a Cray 2. Our system is only about 22× a single processor Cray 2, and hence the primary advantage is our serial and parallel optimizations.…”

Section: Discussionmentioning

confidence: 84%

“…The 3-arm problem had never previously been solved exactly because it was considered infeasible. Indicating frustration with the far easier 2-arm bandit problem, researchers have commented: "In theory the optimal strategies can always be found by dynamic programming but the computation required is prohibitive" [20], and "the space and time requirements for this computation grow at a rate proportional to n 4 making it impractical to compute the decision even for moderate values of say n 50" [9]. Previously, the largest exact 2-arm bandit solution utilized a Cray 2 supercomputer to solve n = 200 [3].…”

Section: Previous Workmentioning

confidence: 99%

Scalable Algorithms for Adaptive Statistical Designs

Oehmke

¹

,

Hardwick

²

,

Stout

³

2000

Scientific Programming

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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.

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“…This is approximately 500,000 times harder than the problem called "impractical" in [9], and 2,000 times harder than that solved in [3] on a Cray 2. Our system is only about 22 a single processor Cray 2, and hence the primary advantage is our serial and parallel optimizations.…”

Section: Discussionmentioning

confidence: 99%

“…Indicating frustration with the far easier 2-arm bandit problem, researchers have commented: "In theory the optimal strategies can always be found by dynamic programming but the computation required is prohibitive" [20], and "the space and time requirements for this computation grow at a rate proportional to n 4 making it impractical to compute the decision even for moderate values of say n 50" [9]. Previously, the largest exact 2-arm bandit solution utilized a Cray 2 supercomputer to solve n=200 [3].…”

Section: Previous Workmentioning

confidence: 99%

Scalable Algorithms for Adaptive Statistical Designs

Oehmke

¹

,

Hardwick²,

Stout³

2000

ACM/IEEE SC 2000 Conference (SC'00)

0

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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.

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A program for sequential allocation of three Bernoulli populations

Hardwick

¹

,

Oehmke

²

,

Stout

³

1999

Computational Statistics & Data Analysis

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We describe a program for optimizing and analyzing sequential allocation problems involving three Bernoulli populations. Previous researchers had considered this problem computationally intractable, and we know of no prior exact optimizations for such problems, even for very small sample sizes. Despite this, our program is currently able to solve problems of size 200 or more by using a parallel computer, and problems of size 100 on a workstation. We describe the program and the techniques used to enable it to scale to large sample sizes. As an illustrative example, 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 metrics. We also indicate extensions of the program that enable it to solve a v ariety of related problems.

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Optimal Bayes procedures for selecting the better of two Bernoulli populations

Cited by 4 publications

References 6 publications

Scalable Algorithms for Adaptive Statistical Designs

Scalable Algorithms for Adaptive Statistical Designs

Scalable Algorithms for Adaptive Statistical Designs

A program for sequential allocation of three Bernoulli populations

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