Minimax-Optimal Static Estimators Under Interference

Abstract

We study the problem of estimating the global treatment effect in randomized experiments under interference, where a unit's outcome may depend on the treatment assignments of other units. We adopt a minimax framework, allowing an adversary to select an outcome function from a class of functions that satisfy bounded outcomes and bounded interference. We derive minimax-optimal static estimators that are robust to a wide range of interference structures, parameterized by a scalar $δ$ controlling the maximum influence of one unit's treatment on another's outcome. Under large interference, we observe two regimes. When the treatment and control groups are equally sized, the minimax-optimal static estimator is the zero estimator. When one of the two groups is larger, the minimax-optimal static estimator is a "half-zero" estimator, in which the outcomes of the smaller group are ignored, and the estimator only considers the outcomes of the larger group.