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Minimax-Optimal Static Estimators Under Interference

  • Arthur Delarue
  • Ilan Lobel
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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.

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Cite

BibTeXRIS
BibTeX
@misc{delarue2026minimaxoptimal,
  title = {{Minimax-Optimal Static Estimators Under Interference}},
  author = {Arthur Delarue and Ilan Lobel},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02048},
  eprint = {2611.02048},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02048},
}
RIS
TY  - UNPB
TI  - Minimax-Optimal Static Estimators Under Interference
AU  - Arthur Delarue
AU  - Ilan Lobel
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02048
UR  - https://arxiv.org/abs/2611.02048
AB  - 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.
ER  -