首价竞价均衡间的干扰：偏差与方差分析
Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
AI总结：
针对在线市场中预算约束导致的A/B测试干扰问题，提出基于市场细分的并行预算控制测试设计，利用首价竞价均衡框架定义干扰，并构建去偏代理与插入式估计器消除一阶偏差，实现渐近正态估计。
摘要：
在线 A/B 测试被互联网行业广泛用于指导新功能发布的决策。对于在线市场（如广告市场），当买方在预算约束下运作时，标准的 A/B 测试方法可能会导致有偏的结果，因为实验中一个分支的预算消耗会影响另一个分支的表现。为了抵消这种干扰，可以使用预算分割设计，其中预算约束基于每个分支独立运作，每个分支获得等额的预算比例，从而实现“预算控制的 A/B 测试”。尽管预算控制的 A/B 测试具有明显的优势，但当预算分割过小时，性能会下降，限制了此类系统的整体吞吐量。在本文中，我们提出了一种并行预算控制的 A/B 测试设计，其中我们使用市场细分来识别更大市场中的子市场，并在每个子市场上运行并行实验。我们的贡献如下：首先，我们在大型在线市场环境中引入并展示了带有子市场的并行预算控制 A/B 测试设计的有效性。其次，我们使用首价竞价均衡（FPPE）框架正式定义了首价拍卖市场中的市场干扰。第三，我们借鉴数学规划中敏感性分析的原理，提出了一种去偏代理，消除了 FPPE 的一阶偏差。第四，我们推导了该代理的插入式估计器，并建立了其渐近正态性。第五，我们提供了一种用于子市场并行预算控制 A/B 测试的估计程序。最后，我们展示了在半合成数据上的数值示例，证实了去偏技术实现了理想的覆盖特性。
英文摘要：
Online A/B testing is widely used in the internet industry to inform decisions on new feature roll-outs. For online marketplaces (such as advertising markets), standard approaches to A/B testing may lead to biased results when buyers operate under a budget constraint, as budget consumption in one arm of the experiment impacts performance of the other arm. To counteract this interference, one can use a budget-split design where the budget constraint operates on a per-arm basis and each arm receives an equal fraction of the budget, leading to ``budget-controlled A/B testing.'' Despite clear advantages of budget-controlled A/B testing, performance degrades when budget are split too small, limiting the overall throughput of such systems. In this paper, we propose a parallel budget-controlled A/B testing design where we use market segmentation to identify submarkets in the larger market, and we run parallel experiments on each submarket. Our contributions are as follows: First, we introduce and demonstrate the effectiveness of the parallel budget-controlled A/B test design with submarkets in a large online marketplace environment. Second, we formally define market interference in first-price auction markets using the first price pacing equilibrium (FPPE) framework. Third, we propose a debiased surrogate that eliminates the first-order bias of FPPE, drawing upon the principles of sensitivity analysis in mathematical programs. Fourth, we derive a plug-in estimator for the surrogate and establish its asymptotic normality. Fifth, we provide an estimation procedure for submarket parallel budget-controlled A/B tests. Finally, we present numerical examples on semi-synthetic data, confirming that the debiasing technique achieves the desired coverage properties.
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