Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

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