Off-Policy Learning of Capacity-Constrained Allocations

We study off-policy learning of capacity-constrained allocations from individual logged rewards under a shared linear model and an unknown logger that may assign zero probability to available actions. Capacity constraints determine which unresolved reward directions matter, captured by a source-radius modulus. We characterize the exact infinite-data identification threshold for a fixed source law and propose a minimax-regret allocation rule with high-probability worst-batch guarantees without overlap or minimum-eigenvalue assumptions. Marginal and integral outputs can have fundamentally different sample complexity. A constructed family requires $\Theta (\log (1/\delta ))$ samples for marginal outputs but $\Theta ({\rho }^{-1}\log (1/\delta ))$ for integral outputs. Experiments recover the predicted finite-sample behavior, and a semi-synthetic study on real LLM query contexts shows lower empirical failure and regret under source ambiguity for MRA than regression and robust baselines.