Primary Submission Category: Policy Learning
Optimal Plug-in Treatment Rules under Heterogeneous Network Interference
Authors: Elena Dal Torrione, Laura Forastiere,
Presenting Author: Elena Dal Torrione*
This paper studies optimal treatment policies under heterogeneous network interference, where treating different individuals affects welfare differently through their direct response and influence on others. In settings without interference, the welfare-maximizing policy treats individuals with positive conditional average treatment effects. Under interference, however, individual outcomes depend on others’ treatments, and simple plug-in treatment rules are generally unavailable without further assumptions on the underlying potential outcome structure. We first derive general first-order optimality conditions in terms of conditional direct effects for units with given covariates and conditional indirect effects on other units. Unlike no-interference settings, we show that under interference optimal treatment rules may be stochastic, and we provide sufficient conditions for when the optimal policy is stochastic or deterministic. Next, we propose a quadratic outcome model that incorporates pairwise treatment interactions and nests standard linear-exposure models. We derive conditions under which the optimal policy admits a closed-form characterization and discuss implications for plug-in treatment rule estimation. Finally, we extend our analysis to welfare maximization under budget constraints and to the complementary problem of minimizing budget subject to outcome constraints.