||Discovery of resource availability distributed at coalition partners is crucial for orchestrating cross-partner software defined coalition (SDC) workflows. For simplicity and privacy control, a coalition partner may adopt a simple feasi- bility interface that has already been deployed in some civilian networks: a client (peer) specifies a vector for the amount of bandwidth for a set of flows, and the partner searches available paths that satisfy policy constraints, and returns success or failure. Whether this interface can serve as the foundation of coalition resource exposure is an important issue. In this paper, we conduct the first study by considering the interface as a membership oracle over a polytope. We leverage efficient oracle construction techniques in optimization and learning theory to develop a learning framework that automatically, and swiftly learns the optimal resource reservations. Using a 7-day trace from a large operational federation network, we show that our design has a 100% correctness ratio. Preliminary results appeared in AAAI 2019.