Batch Active Evidence Acquisition via Submodular Utility Coverage across Hypotheses

Decision systems in clinical diagnosis, fraud review, industrial monitoring, and tool use must choose which costly evidence to acquire before making a prediction. Sequential acquisition selects one action, observes its outcome, and then chooses the next. Test panels, imaging protocols, and related workflows instead require the complete action batch to be selected before any outcome is available. We study this one-shot batch active evidence acquisition setting, where an action can reveal a feature, an image patch, or the answer to a diagnostic question. Without the observation loop, the policy cannot re-estimate the value of the remaining actions after each acquisition, and directly maximizing the expected downstream-loss reduction of a batch is intractable. We introduce hypothesis utility coverage (HUC). Given a partial observation, HUC retrieves similar completed instances to represent plausible completions, transfers their precomputed explanation-derived action utilities, and applies diminishing returns to the utility already covered within each completion. The surrogate is monotone submodular by construction, so greedy selection carries the classical $(1-1/e)$ guarantee on the surrogate under a cardinality budget without assuming anything about the data, and a conditional bound separates its gap from the ideal objective into retrieval, saturation-fit, and utility-estimation terms. On a controlled synthetic benchmark, a matched control shows that the gain over ranking actions by posterior-averaged importance comes from this set-dependent saturation rather than from rescoring individual actions. On diagnostic question acquisition (DDXPlus) HUC improves over a fixed acquisition path at every plotted budget, on real image and tabular datasets the gains are small or absent, and under the reported implementations it is competitive with direct batch scoring at a fraction of the selection cost.