  A/B test, a simple type of controlled experiment, refers to the statistical
procedure of experimenting to compare two treatments applied to test subjects.
For example, many IT companies frequently conduct A/B tests on their users who
are connected and form social networks. Often, the users' responses could be
related to the network connection. In this paper, we assume that the users, or
the test subjects of the experiments, are connected on an undirected network,
and the responses of two connected users are correlated. We include the
treatment assignment, covariate features, and network connection in a
conditional autoregressive model. Based on this model, we propose a design
criterion that measures the variance of the estimated treatment effect and
allocate the treatment settings to the test subjects by minimizing the
criterion. Since the design criterion depends on an unknown network correlation
parameter, we adopt the locally optimal design method and develop a hybrid
optimization approach to obtain the optimal design. Through synthetic and real
social network examples, we demonstrate the value of including network
dependence in designing A/B experiments and validate that the proposed locally
optimal design is robust to the choices of parameters.
