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Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis

Luofeng Liao, Christian Kroer, Sergei Leonenkov, Okke Schrijvers, Liang Shi, Nicolas Stier-Moses, Congshan Zhang

arXiv 11 Feb 2024 · Mathematics — Statistics Theory · 1 citations (OpenAlex)

arXiv:2402.07322 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

43
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in-text mentions
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Vincent Conitzer, Christian Kroer, Debmalya Panigrahi, Okke Schrijve… (2022) Pacing equilibrium in first price auction markets self0.8947471%
2Luofeng Liao, Yuan Gao, and Christian Kroer (2023) Statistical inference for fisher market equilibrium self0.7374450%
3Vincent Conitzer, Christian Kroer, Eric Sodomka, and Nicolas E Stier… (2022) Multiplicative pacing equilibria in auction markets self0.7374350%
4Luofeng Liao and Christian Kroer (2023) Statistical inference and a/b testing for first-price pacing equilibria self0.6939433%
5Yuan Gao and Christian Kroer (2022) Infinite-dimensional fisher markets and tractable fair division self0.6443267%
6Guillaume W. Basse, Hossein Azari Soufiani, and Diane Lambert (2016) Randomization and the pernicious effects of limited budgets on auction experiments0.5112250%
7Min Liu, Jialiang Mao, and Kang Kang (2021) Trustworthy and powerful online marketplace experimentation with budget-split design0.5112250%
8Lihua Chen, Yinyu Ye, and Jiawei Zhang (2007) A note on equilibrium pricing as convex optimization0.5112250%
9Santiago Balseiro, Anthony Kim, Mohammad Mahdian, and Vahab Mirrokni (2017) Budget management strategies in repeated auctions0.40511100%
10Han Hong, Aprajit Mahajan, and Denis Nekipelov (2015) Extremum estimation and numerical derivatives0.40511100%

Showing the top 10 of 43 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Tackling Interference Induced by Data Training Loops in A/B Tests: A Weighted Training Approach0.40511
22501.119960.40511