Budget-First Conformal Robustness Control under Hard Deployment Budgets

Decision-making usually relies on uncertainty sets for robust decisions, and existing methods like conformal robustness control (CRC) typically return an uncertainty set at a fixed coverage or robustness level. However, the uncertainty set may violate pointwise deployment requirements such as per-decision cost limits or set-size budgets. In this paper, we propose *Budget-First Conformal Robustness Control* (BCRC) to satisfy deployment budgets under both continuous and discrete regimes. Our main contribution is a budget-first conformal robustness framework that learns the deployment rule induced by the hard budget. In contrast to this risk-first order, BCRC works backward from the hard budget to construct the maximal feasible candidate set for an observed input. For the resulting budget-feasible deployment, we provide a finite-sample upper bound on the failure probability of the exact deployed rule using an independent certification set. Across various experiments, BCRC consistently satisfies the deployment budget and achieves lower failure risk than several baseline methods under the same budget.