Rerandomization Algorithms for Optimal Designs of Network A/B Tests

A/B testing is an effective method to assess the potential impact of two treatments. For A/B tests conducted by IT companies like Meta and LinkedIn, the test users can be connected and form a social network. Users’ responses may be influenced by their network connections, and the quality of the treatment estimator of an A/B test depends on how the two treatments are allocated across different users in the network. This article investigates optimal design criteria based on some commonly used outcome models, under assumptions of network-correlated outcomes or network interference. We demonstrate that the optimal design criteria under these network assumptions depend on several key statistics of the random design vector. We propose a framework to develop algorithms that generate rerandomization designs meeting the required conditions of those statistics under a specific assumption. Asymptotic distributions of these statistics are derived to guide the specification of parameters in the algorithms. We validate the proposed algorithms using both synthetic and real-world networks.