# D-optimal Design for Network A/B Testing

## TL;DR

This paper introduces a D-optimal design method for network A/B testing that accounts for social network effects using a conditional auto-regressive model, improving experimental efficiency.

## Contribution

It develops a novel D-optimal design criterion incorporating network effects and formulates mixed integer programming solutions for optimal experimental design.

## Key findings

- The proposed method outperforms traditional designs in synthetic network simulations.
- Numerical results demonstrate improved estimation accuracy with the new design.
- Application to real social networks confirms practical effectiveness.

## Abstract

A/B testing refers to the statistical procedure of conducting an experiment 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 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 the 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.