FPGA-accelerated Monte-Carlo integration using stratified sampling and Brownian bridges

M. D. Jong, V. Sima, K. Bertels, David B. Thomas
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引用次数: 2

Abstract

Monte-Carlo Integration (MCI) is a numerical technique for evaluating integrals which have no closed form solution. Naive MCI randomly samples the integrand at uniformly distributed points. This naive approach converges very slowly. Stratified sampling can be used to concentrate the samples on segments of the integration domain where the integrand has the highest variance. Even with stratified sampling, MCI converges very slowly for multidimensional integrals. In this work, we implement an FPGA-accelerated design for MISER, a widely used adaptive MCI algorithm applying stratified sampling. We show how to eliminate the recursion from MISER and partition the algorithm between CPUs and FPGAs. The CPUs manage the control-heavy stratification strategy, while the FPGA is responsible for sampling the integrand. The integrand is compiled into a deep pipeline on the FPGA, producing one function evaluation per clock cycle. We demonstrate the FPGA-accelerated design by pricing a path dependent financial derivative called an Asian option. To make optimal use of the stratification, we implement a Brownian bridge on the FPGA that produces one entire bridge per clock cycle. The FPGA-accelerated design is up to 880 times faster compared to a software reference using the GSL implementation of MISER. Compared to naive MCI in software, our design even requires up to 3572 times less execution time to achieve the same accuracy.
使用分层采样和布朗桥的fpga加速蒙特卡罗积分
蒙特卡罗积分法(MCI)是一种计算无闭形式解的积分的数值方法。朴素MCI对均匀分布的被积点进行随机采样。这种天真的方法收敛得很慢。分层抽样可以用来将样本集中在积分域中被积量方差最大的部分。即使使用分层抽样,MCI对多维积分的收敛速度也很慢。在这项工作中,我们实现了一个fpga加速设计的MISER,一个广泛使用的自适应MCI算法应用分层采样。我们展示了如何消除MISER的递归,并在cpu和fpga之间划分算法。cpu管理重控制的分层策略,而FPGA负责对被积体进行采样。被积件在FPGA上编译成一个深管道,每个时钟周期产生一个函数评估。我们通过对一种称为亚洲期权的依赖于路径的金融衍生品定价来演示fpga加速设计。为了最佳地利用分层,我们在FPGA上实现了一个布朗桥,每个时钟周期产生一个完整的桥。与使用MISER的GSL实现的软件参考相比,fpga加速设计的速度高达880倍。与软件中的原始MCI相比,我们的设计甚至需要多达3572倍的执行时间来达到相同的精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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