EX-ANTE ADMISSION WITH STOCHASTIC PRIORITY COMPETITION: LEARNING WHAT MATTERS

We study an online ex-ante admission problem in which multiple devices compete for a unit-capacity resource through an unknown priority order and stochastic gating mechanism. At each round, the controller observes demand probabilities and selects an admission set before the actual demands are realized. The active admitted devices then compete according to the latent priority order, while the served device generates a stochastic reward with an unknown mean. This setting creates a coupled learning problem: the controller must simultaneously learn reward parameters and acquire priority information from noisy and randomly occurring competition events. We first characterize the full-information admission oracle through a dynamic program and develop an Exact-Priority Two-Phase algorithm based on a sequential noisy priority comparator. We then show that exact recovery of the entire priority order can lead to substantial over-exploration, since many pairwise ordering errors have only limited influence on the admission value. Motivated by a sensitivity analysis of priority misordering, we propose Relevance-Aware Priority-Upper Confidence Bound (UCB), which probes unresolved priority relations only when their potential decision impact remains significant. We establish regret guarantees that capture both statistical informativeness and decision relevance, and derive a complementary decision-theoretic lower bound. Experiments confirm that the proposed strategy substantially reduces unnecessary priority exploration, particularly in regimes with nearly homogeneous rewards, low effective service probabilities, or rare contextual overlap.