  Randomized experiments are widely used to estimate causal effects across a
variety of domains. However, classical causal inference approaches rely on
critical independence assumptions that are violated by network interference,
when the treatment of one individual influences the outcomes of others. All
existing approaches require at least approximate knowledge of the network,
which may be unavailable and costly to collect. We consider the task of
estimating the total treatment effect (TTE), or the average difference between
the outcomes when the whole population is treated versus when the whole
population is untreated. By leveraging a staggered rollout design, in which
treatment is incrementally given to random subsets of individuals, we derive
unbiased estimators for TTE that do not rely on any prior structural knowledge
of the network, as long as the network interference effects are constrained to
low-degree interactions among neighbors of an individual. We derive bounds on
the variance of the estimators, and we show in experiments that our estimator
performs well against baselines on simulated data. Central to our theoretical
contribution is a connection between staggered rollout observations and
polynomial extrapolation.
