Dynamic Finite-Budget Allocation of Stratified Sampling with Adaptive Variance Reduction by Strata
Dynamic Finite-Budget Allocation of Stratified Sampling with Adaptive Variance Reduction by Strata
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DOI：
10.1137/21m1430996
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发表时间：
2023-04
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影响因子：
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通讯作者：
Chenxiao Song;Ray Kawai
中科院分区：
文献类型：
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作者：
Chenxiao Song;Ray Kawai
我们开发并分析了一种动态有限预算分配方案，用于在单位超立方体上进行通用分层抽样，并通过分层应用自适应方差减少。通过对并行任务进行批处理，所提出的方案仅偶尔成功地更新预算分配，但有效地考虑了层方差的减少，同时估计层均值并始终更新方差减少参数。该方案旨在适应参数搜索过程的各种现有算法。特别是，当采用随机近似时，我们根据一路调整的批量大小得出最佳的层批量学习率。提供数值结果来支持理论结果并说明所提出方案的有效性。
We develop and analyze a dynamic finite-budget allocation scheme for stratified sampling for general purposes on the unit hypercube with adaptive variance reduction applied by strata. By batching the parallelized tasks, the proposed scheme succeeds to update the budget allocation only occasionally yet effectively takes into account the decreasing stratum variances while simultaneously estimating the stratum means and updating the variance reduction parameters throughout. The scheme is designed to accommodate a variety of existing algorithms for the parameter search procedure. In particular, when stochastic approximation is employed, we derive optimal stratum batchwise learning rates in accordance with the adjusted batch size along the way. Numerical results are provided to support the theoretical findings and to illustrate the effectiveness of the proposed scheme.