Scalable Policy Maximization Under Network Interference

Many interventions, such as vaccines in clinical trials or coupons in online marketplaces, must be assigned sequentially without full knowledge of their effects. Multi-armed bandit algorithms have proven successful in such settings. However, standard independence assumptions fail when the treatment status of one individual impacts the outcomes of others, a phenomenon known as interference. We study optimal-policy learning under interference on large networks. Existing approaches to this problem require repeated observations of the same fixed network and struggle to scale in sample size beyond as few as fifteen connected units --- both limit applications. We show that common assumptions on the structure of interference enable a parsimonious linear parameterization of the reward function. We develop a scalable Thompson sampling algorithm that maximizes cumulative rewards on a $n$-node network while allowing for both nodes and edges to be sampled at each time period. We prove upper and lower bounds on Bayesian regret that imply near-optimality. Simulation experiments show that our algorithm learns quickly and outperforms existing methods. The results close a key scalability gap between causal inference methods for interference and practical bandit algorithms, enabling policy optimization in large-scale networked systems.