When experimental units are disconnected—such that the treatment of one unit does not influence the outcome of another—the average treatment effect is the main causal estimand, and its value is independent of the experiment design policy. In contrast, networked systems feature interference: interconnected units can influence each other’s outcomes, leading to a proliferation of causal estimands, each dependent on the policy. This introduces a key off-policy estimation challenge: can we estimate an arbitrary causal estimand under a policy different from the one used to collect experiment data?

To address this, we represent causal estimands as Boolean functions and provide unbiased estimators for off-policy estimation. We characterize how assumptions about network interference interact with network sparsity to determine the variance of these estimators. While the variance of any causal estimator—including our off-policy estimators—is generally non-identifiable, we derive unbiased estimators for conservative variance bounds, which tighten under stronger interference assumptions.

Crucially, framing causal estimands as Boolean functions enables a novel perspective: the proliferation of estimands can be seen as providing higher-order corrections in a Taylor expansion of the expected average outcome curve around the experiment design policy. This insight opens up promising avenues for the optimal design of experiments, aimed at estimating the full off-policy curve. We illustrate by reanalyzing data from a prior field experiment on social network spillovers in the adoption of agricultural insurance.