This paper investigates the variance reduction techniques Antithetic Variates (AV) and Latin Hypercube Sampling (LHS) when used for sequential sampling in stochastic programming and presents a comparative computational study. It shows conditions under which the sequential sampling with AV and LHS satisfy finite stopping guarantees and are asymptotically valid, discussing LHS in detail. It computationally compares their use in both the sequential and non-sequential settings through a collection of two-stage stochastic linear programs with different characteristics. The numerical results show that while both AV and LHS can be preferable to random sampling in either setting, LHS typically dominates in the non-sequential setting while performing well sequentially and AV gains some advantages in the sequential setting. These results imply that, given the ease of implementation of these variance reduction techniques, armed with the same theoretical properties and improved empirical performance relative to random sampling, AV and LHS sequential procedures present attractive alternatives in practice for a class of stochastic programs.

中文翻译：

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随机规划中顺序采样的方差减少

本文研究了在随机编程中用于顺序采样时的方差减少技术对偶变量 (AV) 和拉丁超立方体采样 (LHS)，并提出了比较计算研究。它显示了 AV 和 LHS 的顺序采样满足有限停止保证并且渐近有效的条件，详细讨论了 LHS。它通过具有不同特征的两阶段随机线性程序的集合，在计算上比较它们在顺序和非顺序设置中的使用。数值结果表明，虽然 AV 和 LHS 在任一设置中都比随机采样更可取，但 LHS 通常在非顺序设置中占主导地位，同时顺序执行良好，并且 AV 在顺序设置中获得一些优势。这些结果意味着，