Optimal Design under Interference, Homophily, and Robustness Trade-offs

TL;DR

This paper develops a novel framework for optimizing experimental designs in network settings considering interference, homophily, and robustness, using advanced mathematical programming and algorithms, with empirical validation on simulated and real data.

Contribution

It introduces a new potential outcomes model and optimization framework for experimental design that accounts for interference and homophily, solved via SDP and vector-balancing algorithms.

Findings

Optimized designs reduce worst-case MSE in network experiments.

Semidefinite programming and Gram-Schmidt Walk outperform traditional methods.

Empirical results demonstrate improved robustness and accuracy.

Abstract

To minimize the mean squared error (MSE) in global average treatment effect (GATE) estimation under network interference, a popular approach is to use a cluster-randomized design. However, in the presence of homophily, which is common in social networks, cluster randomization can instead increase the MSE. We develop a novel potential outcomes model that accounts for interference, homophily, and heterogeneous variation. In this setting, we establish a framework for optimizing designs for worst-case MSE under the Horvitz-Thompson estimator. This leads to an optimization problem over the covariance matrices of the treatment assignment, trading off interference, homophily, and robustness. We frame and solve this problem using two complementary approaches. The first involves formulating a semidefinite program (SDP) and employing Gaussian rounding, in the spirit of the Goemans-Williamson approximation algorithm for MAXCUT. The second is an adaptation of the Gram-Schmidt Walk, a vector-balancing algorithm which has recently received much attention. Finally, we evaluate the performance of our designs through various experiments on simulated network data and a real village network dataset.