تقرير
Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
| العنوان: | Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis |
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| المؤلفون: | Liao, Luofeng, Kroer, Christian, Leonenkov, Sergei, Schrijvers, Okke, Shi, Liang, Stier-Moses, Nicolas, Zhang, Congshan |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Computer Science - Computer Science and Game Theory, Economics - Econometrics |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.07322 |
| رقم الأكسشن: | edsarx.2402.07322 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |