Optimized Covariance Design for AB Test on Social Network under Interference

Online A/B tests have become increasingly popular and important for social platforms. However, accurately estimating the global average treatment effect (GATE) has proven to be challenging due to network interference, which violates the Stable Unit Treatment Value Assumption (SUTVA) and poses great challenge to experimental design. Existing network experimental design research was mostly based on the unbiased Horvitz-Thompson (HT) estimator with substantial data trimming to ensure unbiasedness at the price of high resultant estimation variance. In this paper, we strive to balance the bias and variance in designing randomized network experiments. Under a potential outcome model with 1-hop interference, we derive the bias and variance of the standard HT estimator and reveal their relation to the network topological structure and the covariance of the treatment assignment vector. We then propose to formulate the experimental design problem as to optimize the covariance matrix of the treatment assignment vector to achieve the bias and variance balance by minimizing the mean squared error (MSE) of the estimator. An efficient projected gradient descent algorithm is presented to the implement of the desired randomization scheme. Finally, we carry out extensive simulation studies to demonstrate the advantages of our proposed method over other existing methods in many settings, with different levels of model misspecification.