Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
Proposes parallel budget-controlled A/B testing with market segmentation and FPPE bias correction, improving estimation accuracy under market interference.
Key Findings
Methodology
This paper introduces a parallel market segmentation-based A/B testing framework, integrating FPPE analysis to address market interference bias. It employs a bias-debiased surrogate derived via sensitivity analysis, constructing a plug-in estimator with proven asymptotic normality. The approach combines market partitioning with bias correction, optimizing statistical efficiency. Core algorithms include FPPE bias analysis, gradient estimation, and market segmentation, enabling multiple parallel experiments with reduced bias and variance. The methodology rigorously models market equilibrium, derives bias formulas, and implements bias-adjusted estimators validated through semi-synthetic experiments, demonstrating substantial bias reduction and improved confidence interval coverage.
Key Results
- On real Meta advertising data, the bias-corrected estimator achieved 81.5% confidence interval coverage, surpassing 70% of uncorrected methods, with a 30% reduction in mean bias. In semi-synthetic simulations, bias decreased by over 30% at sample size t=1000, with confidence intervals narrowing by 20%. The asymptotic normality of the estimator was confirmed, supporting reliable inference. The bias correction effectively mitigates cross-market interference, maintaining robustness across market structures and sample sizes. These results demonstrate the method’s practical utility for large-scale online experiments, significantly enhancing accuracy and reliability.
Significance
This work addresses a fundamental challenge in online market experimentation: market interference bias. By integrating FPPE-based bias correction with market segmentation, it offers a systematic solution to improve the credibility of A/B test results in complex, multi-market environments. The approach enhances the precision of policy evaluation, advertising optimization, and revenue estimation, facilitating more informed decision-making in digital marketplaces. Theoretically, it advances the understanding of market equilibrium estimation under contamination and interference, providing a rigorous framework for future research. Industry implications include more reliable ad targeting, budget allocation, and policy testing, ultimately leading to more efficient and trustworthy online ecosystems.
Technical Contribution
The paper introduces a novel bias-debiased surrogate for FPPE, derived via sensitivity analysis and directional derivatives, enabling systematic bias removal. It establishes asymptotic normality for the plug-in estimator, providing theoretical guarantees for inference. The framework combines market segmentation with bias correction, allowing multiple parallel experiments with reduced interference bias. It also develops efficient Hessian estimation techniques and influence function-based variance estimation, broadening the applicability of FPPE analysis. These contributions significantly extend the statistical theory of market equilibrium estimation under contamination, offering practical algorithms for large-scale, real-world applications.
Novelty
This is the first work to systematically incorporate bias correction into FPPE models under market interference, leveraging sensitivity analysis to derive a closed-form bias adjustment. It innovatively combines market segmentation with bias correction, enabling parallel experiments that mitigate cross-market contamination. Unlike prior studies focusing solely on equilibrium analysis or simple randomization, this approach provides a rigorous, bias-reducing estimation framework tailored for complex, multi-market online environments, representing a significant step forward in both theory and practice.
Limitations
- The bias correction relies on market regularity conditions, such as smoothness and strict slackness, which may not hold in highly irregular or dynamic markets. If market segmentation is inaccurate, residual bias may persist. Computational costs for Hessian and influence function estimation can be high in large-scale settings, requiring further optimization. The model assumes known contamination level α; in practice, estimating α accurately remains challenging. Future work should address these limitations to enhance robustness and scalability.
Future Work
Future research will explore adaptive, online bias correction algorithms for real-time market environments, extending the framework to non-linear and dynamic models. Developing scalable Hessian and influence function estimators will be crucial for large-scale deployment. Additionally, integrating machine learning techniques for market segmentation and contamination level estimation can improve robustness. Further theoretical work on relaxing regularity assumptions and handling non-stationary markets will broaden applicability, ultimately enabling more precise, scalable, and real-time bias correction in complex online ecosystems.
AI Executive Summary
In the rapidly evolving landscape of online advertising and digital marketplaces, A/B testing remains a cornerstone for evaluating new features and policies. However, traditional methods often falter under the influence of market interference, especially when buyers operate under budget constraints and cross-market interactions occur. These issues introduce bias, undermining the reliability of experimental conclusions. Existing solutions, such as budget splitting, mitigate interference but at the cost of statistical power, limiting the scope and scale of experiments.
This paper introduces a novel approach that combines market segmentation with parallel budget-controlled A/B testing, leveraging the first-price pacing equilibrium (FPPE) model. By partitioning the market into submarkets and conducting experiments in parallel, the authors aim to reduce interference effects. To address residual bias, they develop a bias-debiased surrogate derived through sensitivity analysis, which effectively removes the first-order bias inherent in FPPE estimates. The core innovation lies in the analytical derivation of bias formulas, the construction of a plug-in estimator, and the proof of its asymptotic normality, providing a solid statistical foundation for inference.
Empirical validation on real Meta advertising data and semi-synthetic simulations demonstrates that the bias correction substantially improves confidence interval coverage, reaching over 81%, compared to uncorrected methods. The bias reduction is robust across different market structures and sample sizes, confirming the method’s practical utility. Theoretical contributions include the derivation of bias formulas, the development of efficient Hessian estimators, and the establishment of asymptotic normality, which together advance the statistical understanding of market equilibrium under contamination.
Overall, this work offers a rigorous, scalable solution to the longstanding problem of market interference bias in online experiments. It enhances the credibility of A/B testing results, enabling more accurate decision-making in digital advertising, e-commerce, and beyond. Future directions involve extending the framework to dynamic, non-linear markets and developing online algorithms for real-time bias adjustment, paving the way for more reliable and scalable experimental methodologies in complex market environments.
Deep Dive
Plain Language Accessible to non-experts
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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.