D-Optimal Design for Network A/B Testing

  • Victoria Pokhilko
  • Qiong Zhang
  • Lulu KangEmail author
  • D’arcy P. Mays
Original Article
Part of the following topical collections:
  1. Algorithms, Analysis and Advanced Methodologies in the Design of Experiments


A/B testing refers to the statistical procedure of experimental design and analysis to compare two treatments, A and B, applied to different testing subjects. It is widely used by technology companies such as Facebook, LinkedIn, and Netflix, to compare different algorithms, web-designs, and other online products and services. The subjects participating in these online A/B testing experiments are users who are connected in different scales of social networks. Two connected subjects are similar in terms of their social behaviors, education and financial background, and other demographic aspects. Hence, it is only natural to assume that their reactions to online products and services are related to their network adjacency. In this paper, we propose to use the conditional auto-regressive model to present the network structure and include the network effects in the estimation and inference of the treatment effect. A D-optimal design criterion is developed based on the proposed model. Mixed integer programming formulations are developed to obtain the D-optimal designs. The effectiveness of the proposed method is shown through numerical results with synthetic networks and real social networks.


A/B testing Conditional auto-regressive model D-optimal design Mixed integer programming Social network 



We sincerely thank the editor, the handling editor, and all the referees for their insightful comments which helped us improving the paper. This research was supported by US National Science Foundation Grant CMMI-1435902 and DMS-1916467.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Department of Statistical Sciences and Operations ResearchVirginia Commonwealth UniversityRichmondUSA
  2. 2.School of Mathematical and Statistical SciencesClemson UniversityClemsonUSA
  3. 3.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA

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