Exploration under Heterogeneous Feedback:Exact Geometry of Ordered Admission Bandits

Efficient exploration depends on where informative feedback is available, not just which actions offer high utility. We study ordered admission bandits with increasing known utility scales, decreasing unknown survival probabilities, and a strictly unimodal product. Under heterogeneous feedback, the optimum's neighbors need not be the best exploration sources. We reduce the structured-bandit allocation program exactly to a left-prefix constraint and a right-neighbor constraint. The resulting closed form selects the left source by its regret-to-information ratio, recovering neighbor exploration under homogeneous releases and proving an unbounded penalty for enforcing locality under heterogeneous releases. For regular single-candidate count/randomized-response feedback, we develop Certified Oracle Tracking (COT) and prove that suitable fixed tunings approach the lower-bound constant arbitrarily closely. Experiments with 10, 20, and 50 arms demonstrate source migration and competition. On frozen real-data gates, changing only the release channel isolates the value of information location: COT reduces weak-feedback regret by 73.5% against a matched neighbor-oracle ablation, while their full-count trajectories coincide. These results characterize when exploration should move beyond neighbors and provide a certified policy for using that information.