When More Outcomes Stop Helping: The Cost of Interference in Network Experiments

Network experiments can assign treatment broadly while measuring only $B\ll n$ outcomes. Under interference, these measurements need not yield mutually compatible causal observations. We formulate this constraint as a budgeted experiment on a labeled exposure-conflict graph. Including the analysis support in the design record preserves the physical experiment's minimax risk. For Direct and Global effects with bounded second moments on bounded-degeneracy networks, we establish the common decomposition $R_{B,c}(G;M){\asymp }_k{M}^2\{B^{-1}+{\Psi }_c(G)\}$. It separates the $B^{-1}$ cost of outcome measurement from a contrast-specific, topology-dependent risk floor. We develop Design-Supported Conflict-Graph Design (DS-CGD): an offline search builds a finite library of compatible supports, and convex mixture optimization allocates probability using pretreatment residual scores. The resulting exact inclusion probabilities yield a design-unbiased generalized-difference estimator. Across evaluated conditions, geometric-mean Direct-effect RMSE is 12% lower than the best matched baseline in each condition on synthetic graphs, and 16% and 22% lower on the two observed network datasets (CAI and ca-GrQc), respectively. The corresponding Global-effect reductions are 40%, 4%, and 11%.