Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915128511823872 |
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| author | Liao, Luofeng Kroer, Christian Leonenkov, Sergei Schrijvers, Okke Shi, Liang Stier-Moses, Nicolas Zhang, Congshan |
| author_facet | Liao, Luofeng Kroer, Christian Leonenkov, Sergei Schrijvers, Okke Shi, Liang Stier-Moses, Nicolas Zhang, Congshan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis Liao, Luofeng Kroer, Christian Leonenkov, Sergei Schrijvers, Okke Shi, Liang Stier-Moses, Nicolas Zhang, Congshan Statistics Theory Computer Science and Game Theory Econometrics 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. |
| title | Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis |
| topic | Statistics Theory Computer Science and Game Theory Econometrics |
| url | https://arxiv.org/abs/2402.07322 |