  Estimating causal effects under interference is pertinent to many real-world
settings. However, the true interference network may be unknown to the
practitioner, precluding many existing techniques that leverage this
information. A recent line of work with low-order potential outcomes models
uses staggered rollout designs to obtain unbiased estimators that require no
network information. However, their use of polynomial extrapolation can lead to
prohibitively high variance. To address this, we propose a two-stage
experimental design that restricts treatment rollout to a sub-population. We
analyze the bias and variance of an interpolation-style estimator under this
experimental design. Through numerical simulations, we explore the trade-off
between the error attributable to the subsampling of our experimental design
and the extrapolation of the estimator. Under low-order interactions models
with degree greater than 1, the proposed design greatly reduces the error of
the polynomial interpolation estimator, such that it outperforms baseline
estimators, especially when the treatment probability is small.
